It is my belief that many Americans hold to a form of separation of church and state which is not healthy for state nor church. The principle of separation of church and state is more than just a social convention, it is a principle that is supported by both Old and New Testaments. When Saul attempted to take on priestly duties he was rebuked by the Lord. (1 Samuel 13:18) For the New Testament proof we can think of "Give to Caesar the things that are Caesar's and give to God the things that are God's" and Christ's reply to Pilate that His kingdom is not of this world. (Luke 20:25; John 18:36) But at the same time, the idea of separation of church and state in modern American form does not correlate with the Old Testament form because the separation mean in the OT that religion had an influence on the nation corporately. Nor does the American system of separation of church and state by and large approve a voice calling national leaders to see their sin as John the Baptist did with Herod. The American system is not uniform, nor is it's purpose the same in everyone's eyes. For some American's whose belief system is naturalistic, the separation of church and state is a way to minimize the influence of the church in the life of America. In other words, it is a way to allow private citizens to maintain their superstition if they must have it but the goal is to isolate it to the private lives of individuals who are not enlightened enough to see the truth of science. For many religious types of people, the separation of church and state is system to help everyone get along and maintain peace. The separation of church and state in the scriptures has neither of these purposes. Rather purpose is to maintain purity of true faith and the ability to transcend earthly powers.
Ideally in my humble opinion, a healthy separation of church and state has these elements:
1. Public ceremonies that incorporate prayer and oaths should use the denomination/religion of choice of those participating.
2. The state should not seeks to affirm it's temporal power through state sanctified worship. Emperor worship such as in ancient Rome and in pre-WW II Japan, the state confused some of the people into thinking temporal powers had transcendent virtue. The state also robs itself of an absolute moral standard to guide those who serve as government leaders.
3.The church should not attempt to exercise temporal power rather than instruct from the transcendent truth and virtue. When the church exercises temporal power, it over simplifies the gospel to being a loyalty oath. How can the church teach the doctrines of grace when the power it exercises is earthly and temporal? Grace is heavenly and eternal.
4.The church should recognize the state as a tool of the Lord to suppress evil.
5.The state should respect the power of truth that the church offers.
6.There should be a creative tension between church and state rather than a destructive tension. I would define destructive tension as persecution or hate from either the church or the state for the other. The civil leaders should be discipled by the church to have a moral compass. As pragmatic issues are raised by the state, these issues will stretch the church to attain new heights for understanding and applying truth.