I want to at least attempt to discuss the relationship between the Church and civil authority. Since we do have a separation of Church and State – in the sense that the Church is not the State and that the State is the entity charged with keeping order and punishing criminals, it seems germane.
I think that most people would agree that the human being somehow innately understands the necessity and value of societal order and justice that supersedes the individuals desires. Social order reflects a sort of collective consciousness that rises above any single individual's level of perfection in an imperfect world. We know from history that one individual with unchecked power doesn't really work well as a system of government. 'Absolute power corrupts absolutely' is a cliché for a reason.
According to Scripture all 'governmental systems' and civil authorities are established by God and are a necessary concession for the good order of the world because of the Fall. But our 'systems', even if ordained by God, are run by fallen humans. I doubt this fact is lost on anyone.
In his commentary on Romans 13, St. John Chrysostom has this to say about how we should regard civil authority and evil politicians:
“For do not tell me of some one who makes ill use of (the institutions of government) but look to the good order that is in the institution itself, and you will see the great wisdom of Him who enacted this law from the first...whether in punishing, or in honoring, the state is a Minister, in avenging virtue's cause, in driving vice away, as God wills.”
'Systems' of government and societal order are a collective hedge against individual human anarchy which tends toward evil, and it also provides more or less for some definition of 'the common welfare' of the members of society. And, of course, we know that while some systems might be better than others, no system, if occupied by evil people, will keep people from doing evil things.
Every Christian anti-death penalty argument I've seen calls for society to 'forgive our enemies' because Christ calls on us to forgive our enemies. And I would acknowledge that I, as an individual, am called to forgive my personal enemies – which is HARD and I work at it daily, but I don't see that that extends to the State.
The call of the Gospel is ultimately to persons, not institutions. One must have belief in the Gospel to live it, not merely be following laws. While we obey laws because they are laws and there are consequences if we break them and we are caught (think, on the mild end of the spectrum, speed limits), our faith cannot work that way. A person can, theoretically, be forced to obey all the strictures of a faith, down to the last 't', but that doesn't give them faith. It doesn't make them a believer, and in the case of faith and religion, at least, it's the belief, the inner desires and thoughts that count. After all, God's Kingdom is not of this world.
All that being said, it is appropriate for the State to legislate against evil for the very same reason Noah was commanded to institute the death penalty – we are created in the Image of God. The God ordained order of the State, at some level, reflects the image of God in that it exists for the 'good of society' which calls for defining good and evil through civil law.
In the Old Testament, God dealt with human beings on a revelatory moral and religious level through Judaism and the Law. Even if one views Judaism as only a shadow of the Gospel, it was still God ordained, and carries some merit. The first layer of Godly order laid down into the moral chaos of the fallen world? Judaism was a revelation to the world of universally applicable moral and ethical precepts, and it included the death penalty. These aspects of the Law (I believe) which included capital punishment apart from the fullness of knowledge and belief in the Gospel are still a functional way to order a non-Gospel based human society. We in the modern world may (and do) disagree with the Law over who (and for what and how) should be put to death, but from Genesis to Revelation the overarching principles of law and order that include justice, fear of consequence, punishment and restraint that deal with evil are universally recognized to be necessary for civil order.
As far as I can see, nowhere in the New Testament is the State held to the standards of the Gospel in how it orders our society. Since inception the Church has existed and functioned within many diverse political systems – some good, some bad, some out and out evil. We don't find the New Testament writers confusing the roles of the Church and the State in the lives of people, most likely because in the times of the New Testament the State was either indifferent or actively hostile to the Church.
The Apostles held up no political system as 'the one true party' and Christians are constrained to pray for all civil leaders, godly or not. Jesus Himself told Pilate as he was condemning Him that he had no power except that which was given him from God. In Romans 13, St. Paul (who was persecuted under both Jewish and Roman law) teaches us that the State has the God ordained responsibility to punish the evil doer and even to exact capital punishment if deemed necessary. St. Paul, in spite of the injustices he personally suffered, doesn't even deal with the possibility of civil law being unjustly administered. He doesn't seem to have an issue with the possibility of the State being in error or unjust at times. Both he and Christ personally stood above the civil order and the injustice they suffered and in so doing personally transformed the world around them without legislating 'Christian values' through governmental systems.
The ancients understood that their moral and religious frameworks were not easily divorced from civil concerns, and throughout Church history it has always been considered, by most Christian expressions, a possibility to have a Christian State. Israel's history is the story of the 'Christian State' imperfectly administered by kings who would bring either blessings or curses upon the people depending on their actions. It was never a utopia, but it was an integration of Church and State. In light of this history the 'prophet/king' relationship and the wielding of power in their respective spheres is quite natural and has yielded, at times, good outcomes for the citizenry. However, it is also clear from Church history that religious coercion by the State does not generally yield good results.
The Church as State is untenable and cannot be justified scripturally or pragmatically. For an example we can look at John Calvin's Geneva to see how his theology of Church and State worked out in practice and what you see can best be described as a 'Christian Taliban'. The failure of Church as State doesn't mean, however, that the State can't or shouldn't align itself with the Gospel. However, it must be understood that there are boundaries between the roles of the Church and the State and not all of the Gospel's demands on the Church and the individual Christian can be integrated into a civil order. The mission of the Church in the world does not cancel God's divine order that the evildoer is restrained by means of the State. I'm not going to go into detail, but one only needs to look at the history of the Church as a State to know that it doesn't work. Theocracy is a bad idea – we loose something in the process. Men use the 'divine right' of their leadership to take advantage. Not all of them, no, but enough, and yes, that happens in secular states too (the corruption), but it's much harder to see and fight when 'God said I could do this'. Look at any of the cults in the world to see this in miniature. Or heck, lets take a brief sidetrack look at Saudi Arabia. Wonderful place. Very religious. Because they don't have a choice. It's a nice, dry place where girls can burn to death because they're not wearing their abaya. Because they're trying to flee a *burning building*! (takes a deep breath) We don't need to look very hard or very far to find historical or modern proof that theocracies don't work.