Hrm... first to the OP, religious principles are like how Vtekkid pointed out: all men are created equal... inalienable rights, etc. Biblically speaking, this refers to how we are all sinners and all fall short of the glory of God. I can expound more but will leave it at that for now.

As for the separation of church and state, it was not to keep the religion out of state affairs but to keep the state out of religious affairs. Religion is very much like race if you want to draw the analogy... A person is who they are and to say that a person can separate themselves from what it is they are, then that's impossible... (like asking a black person to remove their blackness while in public office... can't be done). Religion really is that personal to those who pursue it.

On the other hand, the separation of church and state was so that the state could not mandate a religion upon it's people, such as what the King of England tried to do to the colonies. (If I recall, the King was Catholic and the colonies were largely Protestant... but don't quote me on that)

In regards to the country being founded on christian principles, you need only look at those who wrote the Constitution to base your judgement.