Much has been said on this subject and it has been taken out of context so often that many people believe it to be in the US Constitution. But is not. The phrase “separation of church and state” comes from a letter from President Thomas Jefferson written to the Danbury Baptists Association. This is what that letter says and what the Constitution means with the Establishment Clause.
Believing with you that religion is a matter which lies solely between Man & his God, that he owes account to none other for his faith or his worship, that the legitimate powers of government reach actions only, & not opinions, I contemplate with sovereign reverence that act of the whole American people which declared that their legislature should ‘make no law respecting an establishment of religion, or prohibiting the free exercise thereof,’ thus building a wall of separation between Church and State.
This means that the Legislature (Congress) cannot make a National Church. The “American Church”, the “Church of America” like the English did with Queen Elizabeth I and the Church of England.
The Establishment Clause is fully meant to keep government out of religion, but not religion out of government.