Since early Christianity arose during a time called the pax romana (Peace of Rome) from around 30 BCE to 180 CE, being nonresistant in the army might not be as difficult as one might think. Often times the soldiers would double as construction workers, repair men, postal deliverers, etc. But that doesn't mean soldiers were never faced with the choice to compromise. Martin of Tours is one great example who threw down his arms rather than do violence. And when they did refuse to do the State's bidding of violence or the worship of gods, they were often killed.
If one still wants to hold a pacifist's feet to the fire (something a pacifist would never do) on this, they run into a huge moral issue. The Apostles - especially Paul - had plenty of opportunity to tell slaveholders - people who owned and objectified other human beings - to give up their slaves. In fact, there's a book of the Bible, Philemon, which is solely dealing with a master and his slave. But Paul never tells the slaveholder to release his slave. Rather, he tells the master to accept his slave back, and most importantly, treat him with love like a brother.
Paul was not looking to upend the social structure of Rome. The issue for Christians saturated with the gospel and the fresh image of Christ and his sacrifice was that their lives and positions meant nothing. If they were slaves, so be it. If they were abused by fellow Christians, absorb the cost and don't take them to court. If you're a wife to a non-believing husband, show him love. If you are living in an oppressive government that persecutes you, submit and be good citizens. The important thing was the gospel of love.
John Howard Yoder, in his book "The Politics of Jesus," sums up this notion of the gospel's way to go about addressing our position and seeking social justice.
"[Paul's] first element of counsel is to remain in the social status within which one is; 'in whatever state each was called, there let him remain with God' (v. 24). This applied to the slave's remaining a slave, to the single person's remaining single, to the married woman's remaining with her unbelieving husband, to the forsaken married woman's remaining unmarried without her husband as long as he lives; to accepting one's status as circumcised or as not circumcised. The reasoning supporting this general admonition is not that to change in any of these ways would be sinful or wrong, in the sense of an infraction of the law of God. The concern of the apostle is rather to assist everyone to remain 'free from anxieties' (v. 32), in a world whose structures are impermanent, and not so important that we should concentrate our efforts upon changing our status with regard to them. ('The appointed time has grown very short; from now on let those who have wives live as though they have none...for the form of this world is passing away' [vv. 29-31].)...
Yet right alongside this concern for that freedom which is maintained by not being rebellious about one's status in the present, there runs a second strand of instruction which seems at first to be opposed to it. If a slave can become free, he should avail himself of this opportunity (v. 21). If the husband of the forsaken woman dies she is free to remarry (v. 39); if anyone is strongly inclined toward marriage, that is quite proper (v. 36), but a freed man must not become a slave since that would be to move away from rather than toward freedom (vv. 22-23). Thus the Christian is called to view social status from the perspective of maximizing freedom. One who is given an opportunity to exercise more freedom should do so, because we are called to freedom in Christ. Yet that freedom can already become real within one's present status by voluntarily accepting subordination, in view of the relative unimportance of such social distinctions when seen in the light of the coming fulfillment of God's purposes... The apostles rather transformed the concept of living within a role by finding how in each role the servanthood of Christ - the voluntary subordination of one who knows that another regime is normative - could be made concrete. The wife or child or slave who can accept subordination because 'it is fitting in the Lord' has not forsaken the radicality of the call of Jesus; it is precisely this attitude toward the structures of this world, this freedom from needing to smash them since they are about to crumble anyway, which Jesus had been the first to teach and in his suffering concretize."
Now, if you begin to make these prescribed changes in yourself. If you begin to live free despite your circumstances, and without a focused agenda of toppling structures and regimes. If you follow what the apostles tell you and you pray for kings (even evil ones) and submit to their rule, the apostles don't have to say outright that you shouldn't be a zealot. If you are a slaveholder and you are told to love everyone - including your human property - as brothers, you don't have to attack slavery head on and upend that institution. And if you tell soldiers to do no violence, you don't have to tell everyone to quit being soldiers or not to join the army. We moderns have it backwards as we tend towards the pursuit of legislation to change hearts. Maybe the apostles didn't attack institutions like slavery or the army head-on because doing so could have labeled them as subversive to the national good. But I think the Apostles understood that rather than changing legislation and abolishing institutions in order to change hearts, changed hearts would undermine evil institutions and evil within institutions.