This country was built upon the idea of being able to practice whatever you believe in. People came here to escape being forced to follow a religion they didn't believe in. So why would we turn back now? Religion shouldn't be forced on anyone. Your beliefs are not my beliefs, and my beliefs are not your beliefs. If the church was brought into politics, we'd have even more political chaos and separation than we do now.
For people who believe in religion, the church is necessarily a part of politics. Any major decision a person makes has to be reconciled with their religious beliefs. There is nothing wrong with this, since people have a right to vote fro anything they choose. Although the government can't forbid anyone from following a religion, people can still use their sense of morality to influence their political decisions.
That there is a separation of Church and state. People can use their religious views when they are voting but the actual Church has no business in politics. Once the Church gets involved it is no longer a fair and equal government. People who are not in the Church would be left on the outside looking in which defeats the purpose of a democracy.