While house church theology and the American political left may disagree on a long list of issues, they are in lock step on the question of the separation of church and state--but for completely different reasons.
One might look at separation in a number of ways. We Christians are told that we must separate from the world (Isa. 52:11, Rom. 12:2, 2 Cor. 6:14-18). Further, it is clear in such passages as Jn. 1:12 that becoming a disciple of Christ must be a matter of individual, informed choice. Therefore every individual--whether he be Christian or not--must be allowed to choose Christ (see box, below) or reject Christ. That is, there must be both freedom of religion and freedom from religion.
"Choosing Christ" is a Christian idiom that needs to be understood correctly, as it is actually very poor theology when improperly nuanced. The Scriptures are definite that it actually works the opposite way--God choosing us (Jn. 6:44). The act of "choosing" is a human work, and that humans can do any good thing that would put God in their debt (Rom. 11:34, Eph. 2:9, etc.) is a heresy called "Pelagianism." But Jn. 1:9 says that the advent of Jesus Christ brought in an era in which God confronts every man and woman every moment of every day, drawing him or her to Himself (this is the way Augustine understood it as revealed in his Confessions). So the question is not how we choose, but how we respond to a God who loves us first.
The phrase also tends to reduce being "Christian" to mere intellectual assent. The fate of that sort of Christian may be found in Mt. 7:21-23 and Mt. 25:31-46. Jn 17:3 says that eternal life is for those who know "the only true God and Jesus Christ." The biblical use of the verb "to know" is always relational, never cognitive. So one does not "choose" Christ--one has a relationship with Christ.
This opens up a host of issues regarding the nature of the Christian's obedience to the state and participation of in the state. Those matters concern ethics more than theology, and will not be examined on this page. They properly belong to the process of "binding and loosing" that lies at the heart of our doctrine of church. But the testimony of the Scriptures is clear--when the state compels its citizens to renounce their Lord and their God, the true believer will resist with every ounce of his being. Many, many martyrs have demonstrated this point by making the ultimate sacrifice.
Phil. 3:20 tells us that, when a person becomes a believer (an event that the New Testament equates with joining a church through baptism), he or she becomes a citizen of the kingdom of heaven and no longer a citizen in the country of birth. That may sound like an extreme statement, but it fits well with Jesus' rejection of any political interpretation of his purpose or ministry (Mt. 4:8-10, Mt. 22:15-22, etc.). That the early church took this concept very seriously is evident in a very early letter, called "The Epistle of Mathetes to Diognetus":
...The Christians are distinguished from other men neither by country, nor language, nor the customs they observe. For they neither inhabit cities of their own, nor employ a particular form of speech, nor lead a life which is marked out by any singularity. The course of conduct which they follow has not been devised by any speculation or deliberation of inquisitive men; nor do they, like some, proclaim themselves the advocates of any merely human doctrines. But, inhabiting Greek as well as barbarian cities, according as to the lot of each of them has determined, and following the customs of the natives in respect to clothing, food, and the rest of their ordinary conduct, they display to us their wonderful and confessedly striking method of life. They dwell in their own countries, but simply as sojourners. As citizens, they share in all things with others, and yet endure all things as if foreigners. Every foreign land is to them as their native country, and every land of their birth as a land of strangers.
There is a final footnote to the question of church/state separation. A good case can be made that a society that obeys "Christian" rules of conduct is a healthier society. That may or may not be good social engineering, but it is very bad theology. There is no possible way that one can make a theological case for the objectives of God being achieved through the state. God can use an evil state to accomplish his intentions (Rom. 8:28) as he did with Cyrus (2 Chr. 36:22-23), but the notion that any form of political system can bring in the glorious kingdom of God is a post-millennial view that few hold today.
Rom. 13:1-7 is often used to make this sort of argument, but it is very poor biblical exegesis to snatch those verses out of the material that embraces them. Paul is telling the Roman house churches that they must overcome evil with good (Rom. 12:21), and being model citizens of the state (a state that Paul surely regarded as evil) is one way to accomplish that. Please do not read Rom. 13:1-7 as saying that the state is an alternative ministry of God to the world. See John Howard Yoder, The Politics of Jesus (Grand Rapids: Eerdmans, 1972), 197; James McClendon, Systematic Theology--Ethics (Nashville: Abingdon, 1986), 309-310; Dietrich Bonhoeffer, The Cost of Discipleship (NY: Collier Books, 1959), 294.