The early church is very enlightening on this aspect. They seem to view the state as an entity to whom they can submit, but not an entity for whom they would sacrifice core Christian values. You can see this in a number of the quotes on soldiers and magistrates from Section 4. You may also be able to pull such a notion from Luke 3:6 - one of the passages some use at times in an attempt to disprove pacifism (see an expounding of the passage here). If early soldiers were told that they can continue soldiering, but that in their soldiering they were to do no violence, that has serious implications for our justification of violence - even in positions of governmental authority - today.
Beyond the early church teachings of doing no violence, which extended even to soldiers, it is good to take another look at Romans 13. To do this, you really need to begin reading well before chapter 13. When you look back to chapter 12, Paul is telling Christians to be living sacrifices. To live as an offering to God leads to these actions of not cursing others, blessing those who persecute us, not repaying evil for evil, not taking revenge, leaving wrath to God and trusting his judgment, giving food and drink to our enemies, and overcoming evil with good. That is the Christian call to be a living sacrifice.
Immediately following all of these commands, Paul addresses the government in Romans 13. Interestingly, Paul shifts his language. Instead of using the "you" and "you understood" language of Romans 12, Paul uses "they" language when talking about governments. You, the Christian, are supposed to do all of these self-sacrificial things. But they, the government, the rulers, the authorities, they bear the sword, and we can be ok with them doing that. Just as God was in control when evil Assyria bore the sword for God's purposes (Is. 10), not out of obedience, but in God's sovereignty, so it is with governments today. God is in control over them and he has given them the sword to bear. It is not for we Christians to bear. How could we bear it and continue to be the sacrifice we're called to be in Romans 12? So give taxes, revenue, respect, honor, or whatever else is owed (notice that violence isn't on the list). We'll respect government's God-given authority. But for God's sake - as sacrifices to him - don't give them what they don't deserve. We can do this in faith because God "establishes" (a better interpretation is likely "orders" or "files") even the most powerful governments, and is able to use and bring good about in any circumstance. We are to give vengence over to God (Rom. 12) and trust that he will bring about our good (Rom. 10) regardless of how powerful the evil of our day seems to be.
As if to put an exclamation point on this, Paul immediately shifts back into the "you understood," "you," and "we/us/our" language after discussing the government. And what is the topic at hand immediately following the short remarks on the government? Paul immediately jumps back into how we are to love others and how we are to do no harm.
Despite the whole context of Romans 13, I think what keeps people from reading it consistently is their perception that the few verses which deal with government seem to speak positively about it. Yet that is only true if you discard a deeper understanding of the Bible's language. Many Christians seem to think that Romans labeling authorities as "God's servants" is an affirmation of authorities as a good we should seek. Yet such an assumption makes readings of the prophets difficult when we see Nebuchadnezzer of Babylon is called "God's servant," (Jer. 27:6 and 43:10) or when we see Assyria as a judging tool of God who is then judged for their ruthlessness (Is. 10). Language of one's servanthood does not necessarily connote allegiance of the servant, but is rather an affirmation of God's sovereignty. Regardless of one's actions or intent, God sovereignly controls the outcomes (see Joseph, Jesus, etc). As we step back and view Romans more broadly, Paul talks about God's faithfulness in all circumstances (Rom. 10), moving specifically to his faithfulness to those in exile (Rom. 11). In Romans 12 he asks us to lay down our lives and not conform to the patterns of the world - including not repaying evil or doing bad, even to enemies - in light of the fact that God ordains both the past and the present. In Romans 13 Paul declares that even the authorities who likely seemed out of control or unjust, are servants of God in the sense that God is sovereign even over kings. Yet we are to remain faithful in love, knowing that ultimate justice will one day come at the Day of the Lord.
For those who have never read Romans 13 in context, this idea can be rather foreign. That foreignness is heightened by our culture which emphasizes the importance of tapping into the power of the government, particularly through politics. While I think it is clear that Christ came to establish his political enterprise, the Kingdom, to which we are to have our primary allegiance, most do not see that. Most feel as though - at least in the democratic West - politics and religion don't often have competing allegiances. Fortunately, I think I can point to another passage that makes my case for Romans 13 even clearer - I Corinthians 6:1-6. I will put the text of this passage below and highlight the items I want to emphasize.
"If any of you has a dispute with another, do you dare to take it before the ungodly for judgment instead of before the Lord’s people? 2 Or do you not know that the Lord’s people will judge the world? And if you are to judge the world, are you not competent to judge trivial cases? 3 Do you not know that we will judge angels? How much more the things of this life! 4 Therefore, if you have disputes about such matters, do you ask for a ruling from those whose way of life is scorned in the church? 5 I say this to shame you. Is it possible that there is nobody among you wise enough to judge a dispute between believers? 6 But instead, one brother takes another to court—and this in front of unbelievers!"
Some might point out that Paul is dealing with more trivial cases here in I Corinthians. He is dealing with what seem to be lawsuits. How then does this compare to Romans 13 where we're talking about weighty matters like bearing the sword? Because if believers are being told by Paul that the very government which is bearing the sword against them should be given taxes and respect because God is sovereign over that authority, then certainly this governmental authority extends down through the whole system. Certainly Paul didn't mean that God has only given authority to Caesar, and not to any governmental extensions (e.g. courts). The very system Paul is referencing here in I Corinthians is a part of the government Paul is referencing in Romans 13. And how does Paul talk about that system? Beyond a shadow of a doubt he distances believers from the system. Just look at the way he talks about the church (green) and the government (red). The church - the Kingdom - is the political affiliation for believers. The government - while it is to be given the respect and taxes and whatever else it's due, so long as it doesn't conflict with the Kingdom's affiliation - is for the non-believers. While Romans 13 doesn't have the explicit language of distancing found in I Corinthians 6, there seems to be a shift from the we/us/you (the church) language to a they/them/the rulers sort of language. I Corinthians 6 similarly deals with government interactions, and it is written by the same author as Romans - Paul.
Some may retort that Paul is simply being descriptive in I Corinthians 6, and not prescriptive. He is just identifying that the current governmental system is filled with unbelievers, which only makes sense since Christianity was very new. But this lack of believers in the government at the time of Paul doesn't mean he didn't think Christians should enter coercive governmental positions. But arguing such ignores the first three centuries of early church understanding on the issue. When you have the great majority of voices telling soldiers to quit or do no violence, elders telling magistrates to do no violence, an ecumenical council chastising a return to the army, etc - it helps to show that Paul's words here aren't simply descriptive. Paul's distinction of Christ's political Kingdom and the world's kingdom makes sense if Christ established his Kingdom when he walked the earth. Christ's Kingdom isn't some ethereal, esoteric, future oriented thing. Yes, the Kingdom hasn't fully come yet. Christ is making his enemies his footstool. But he's doing so through the politic he established in his Kingdom, the church. We are Christ's, and we cannot serve two masters.
If there was any doubt as to the reading of Paul's writings, Peter seems to clarify things even further by writing the book of I Peter, which focuses on the issue of authorities, submission, suffering, and love. It's really an invaluable book to go through when trying to discern what the Bible says about these aspects of the Christian life. Unfortunately, most tend to just cherry-pick the notion of submitting to authority in I Peter 2 without first looking at the context, and without understanding that submission is different than obedience. This is why Peter and Paul can ask wives to submit to husbands (even unbelievers) and slaves to submit to masters, and is why Christians are asked to submit to a government that is unjust. In context, I Peter continually tells us that we are subjects and servants of God first. We are exiles and strangers here. But while we serve God wholeheartedly and without compromise, we can acknowledge God's sovereignty over authorities and give them honor and respect. This is true even when authorities and institutions are unjust - like a persecuting government, an unbelieving husband, or a master of slaves. This is true whether the persecution is for religious reasons or not. Apart from suffering for doing evil, our suffering here is in the hands of God. Suffering without doing evil, without retaliating, and with a trust in God's justice is what Christ did, and it's what we are called to do as we walk in his steps. I don't want to tear apart the whole book, so I am just going to put some of the themes I think you should look at as you sift through I Peter yourself.
Political Allegiance and Authorities: I Peter distinguishes sharply between God's Kingdom and humanity's kingdom. It even uses political language to distinguish the two (as do the gospels).
We are strangers in this world (1:1)
Live as strangers (1:17)
We are aliens and strangers in the world (2:11)
Submit to the world's authority so we can remain blameless and not tarnish Christ (2:13-15)
Give honor to kings, but we are to serve and fear God (2:16-17)
We are being built spiritually (2:5)
We are a holy nation (2:9)
Christ is our Lord (3:15)
The church (our Kingdom institution) shouldn't be coercive and Lord power over others (5:3)
Suffering: Suffering in I Peter is called for because Christ suffered. Just as he suffered to heal (2:24), so our suffering can heal (3:1-2 / 4:8). God is in control of suffering. He doesn't want us to suffer for doing the wrong thing, but even if we suffer when not doing the wrong thing, we can take joy in knowing that God is sovereign and will bring justice.
Trials result in rewards on Christ's return (1:8)
Prophets said that Christ would suffer (1:11)
We are redeemed through blood (1:19)
Submit to suffering because Christ did and we follow in his footsteps (2:21-22)
Submit to suffering from unjust authorities - even for non-religious reasons - because of God (2:18-20)
Submit even to unjust authorities so that non-believers might believe (3:1-2). Live blameless for the sake of the pagans (2:12)
You're blessed if you suffer for/while doing right (3:14)
Take on suffering because Christ suffered (4:1)
Those who suffer are in God's control (4:19)
Judgment: Judgment in I Peter is viewed as a future event, but an event that is determined by what occurs now. Believers who endure suffering and are obedient to God, while experiencing pain and some sense of judgment now (I Pet. 4:17), are being purified. Their actions also influence the lives of others, especially unbelievers. Those unbelievers who don't endure sufferings on behalf of God and in the footsteps of Christ Jesus don't escape judgment and purification, however. Their judgment is future oriented and God will exact that judgment perfectly. It is not for the believer to take into their hands here and now.
Trials and suffering will perfect our salvation (1:9)
We are purified through obedience to pure love (1:22)
Pagans will be judged by God (4:5)
God will lift the humble up in due time (5:6)
Christ will restore with his power (5:10)
Resistance and Defense: Coercive force is viewed in a bad light (5:3) when done by the church, and we are told not to repay evil with evil. The only time resistance and force are used for the Christian here is where we are told to resist the Devil - a spiritual battle rather than a physical one. Time and time again the physical is downplayed - not in a gnostic sense as if the physical is bad - but in the sense that our battle is not with flesh and blood. Christ's Kingdom is not of this world and violence in this world is not to be a part of Christ's work here.
Shielded by God (1:5)
Prepare our minds for action (1:13)
War is being waged on our souls (2:11)
No retaliation to injustice but leave to God's judgment (2:23)
Do what is right without fear of unjust authorities (3:6)
Don't repay evil with evil (3:9)
God controls all authorities (3:22)
Cast our cares on God and resist the Devil (5:9)
I saved resistance and defense for last because there is a really awesome part of this particular point. In I Peter 3:10-12 we find Psalm 34 quoted. Undoubtedly, those who heard Peter's words likely knew that Psalm well and could fill in what Peter left out. I will put that psalm in its entirety below. When you look at it, notice the language (I will bold some of the most interesting parts for my emphasis). It is all about God's people taking refuge in him. God does all the fighting and all the protecting and all the justifying. It is about complete trust and dependence on him for justice through a resting in him, by taking on the means of Christ - suffering love. God defeats evil, and he uses the wicked to slay the wicked (vs. 21)
1 I will extol the Lord at all times;
his praise will always be on my lips.
2 I will glory in the Lord;
let the afflicted hear and rejoice.
3 Glorify the Lord with me;
let us exalt his name together.
4 I sought the Lord, and he answered me;
he delivered me from all my fears.
5 Those who look to him are radiant;
their faces are never covered with shame.
6 This poor man called, and the Lord heard him;
he saved him out of all his troubles.
7 The angel of the Lord encamps around those who fear him,
and he delivers them.
8 Taste and see that the Lord is good;
blessed is the one who takes refuge in him.
9 Fear the Lord, you his holy people,
for those who fear him lack nothing.
10 The lions may grow weak and hungry,
but those who seek the Lord lack no good thing.
11 Come, my children, listen to me;
I will teach you the fear of the Lord.
12 Whoever of you loves life
and desires to see many good days,
13 keep your tongue from evil
and your lips from telling lies.
14 Turn from evil and do good;
seek peace and pursue it.
15 The eyes of the Lord are on the righteous,
and his ears are attentive to their cry;
16 but the face of the Lord is against those who do evil,
to blot out their name from the earth.
17 The righteous cry out, and the Lord hears them;
he delivers them from all their troubles.
18 The Lord is close to the brokenhearted
and saves those who are crushed in spirit.
19 The righteous person may have many troubles,
but the Lord delivers him from them all;
20 he protects all his bones,
not one of them will be broken.
21 Evil will slay the wicked;
the foes of the righteous will be condemned.
22 The Lord will rescue his servants;
no one who takes refuge in him will be condemned.
I Peter clarifies even further what we find in Romans 13. A reading of Romans that views the authorities who bear the sword as distinct from the church is not anomalous. And if I Corinthians 6 and I Peter didn't make that clear enough, we have the first three centuries of church history and the first ecumenical council to reinforce such a reading (see section 4 on the early church teaching).
The texts of scripture, when read in context, seem to provide a very plausible reading for the notion of a separate church and state. But to put the final nail in the coffin, I want to undermine this common notion that people seem to have when they read Romans 13 - the idea that God given authority is a good thing. I want to provide three references to show you that this is not the case.
Isaiah 10: We see that Assyria holds the "club of [God's] wrath." That sounds similar to Romans 13's bearing of the sword. But when we read Isaiah 10, we see that while God uses Assyria for judgment, God ends up judging Assyria because their hearts and their methods are wicked.
Luke 4: There is some contention here about what Satan means when he says that he has been given authority. Nevertheless, it seems apparent that he has authority over the earth to at least some extent, or his temptation to Jesus wouldn't really have been a temptation. We can reference other stories, like Job, and see that God does indeed give Satan authority to some extent to do as he pleases. The fact that Satan has this God given authority, however, does not make his actions good.
John 19: Pilate seems to be becoming more frustrated with Jesus, as Jesus isn't helping himself out. Pilate tells Christ that he holds his life in the balance, but Jesus tells him that Pilate has no authority except what he has been given. When we read this in light of Acts 2 where we see that the crucifixion was God's plan, but enacted by evil men, we're left with an understanding that though Pilate had God-given authority and power in this situation, he will still be judged for its use. Though his act accomplished God's purposes, he will still be judged.
I want to argue that the contextual reading of Romans 13 makes much more sense as a Kingdom vs. kingdom reading. Christians aren't being taught how to be a part of government. They're taught the role of the Kingdom and then told to submit to government as far as they can, and to trust God in his sovereignty beyond that. Christians can trust that the sword wielded by the government is ultimately good because God is always behind authority. But this by no means indicates that God condones what or how the authorities do what they do. Romans 13 is a passage of description and hope, not a passage of prescription or a call to marry the kingdom with the Kingdom.
In summary, the main passage in view, Romans 13, discusses government, but surrounds it with the notion of love, self-sacrifice, mercy, doing no evil, and doing no harm - even to enemies. This sandwiched passage on government is an excursion away from Paul talking to the believers about what they should do, and explaining what this separate entity - the government - does. His intention is to affirm God's sovereignty over governments, even the most evil ones, which the persecuted Christians much needed to know. The Bible has always advocated seeking the welfare of the city in which we live, which extended even to exiles in Babylon who were ripped from their homes illegitimately and found themselves living under the rule of another kingdom. But even as they sought the welfare of this foreign country that was now their temporary home, they were not to break with God's law. We see this very clearly in the story of Daniel and his three friends. The same is true for we Christians today. Our allegiance is to the Kingdom, and we are to live under the rule of our king. I can pay taxes to my government. I can respect their authority and submit to them. But to bear the sword against my enemy is to accept an allegiance to the wrong kingdom. I Corinthians 6 helps to highlight this distinction as Paul separates the church from the coercive arm of the secular government. God in his sovereignty can use this secular kingdom to restrain evil with evil - with violence. He did it through Assyria - a despicably wicked nation - in Isaiah 10. God's sovereignty gives me hope and it helps me to trust in his provision that even in evil, God has control. But while God is sovereign even over the hearts of humanity and the evil they do, God has not given me charge to use this evil over which he is sovereign in an attempt to bring about good. While God can use governments to judge as he did with Assyria, he can also judge those governments. God's use of a vessel for his purposes does mean he places a stamp of approval on them.
This was one of the most difficult concepts for me to wrap my mind around, I posted a video below which helped me to understand the role of the church vs. the state. I think it's important to understand that I am not advocating retreat or isolationism. I'm also not saying that Christians shouldn't be involved in institutions or endeavors like education, art, etc. What many pacifists are saying is that at least at a certain level, governmental allegiance conflicts with our Kingdom allegiance and God's expectations for his people. When we begin to do violence to our enemies and use coercive force, we are no longer living as our King would have us live in his Kingdom - a Kingdom he makes available now and wants to show off to the world through the church. The video below is a little choppy, but you can draw the important ideas from it you need. I also wrote a bit more about Romans 13 awhile back. If you'd like to think about it a little more, you can follow this link.