Nowhere in the Constitution are the words "separation of church and state" found. The idea of a wall separating church and state comes from a letter written by Thomas Jefferson to a group of Baptist pastors who were concerned that the new government would force states to adhere to some kind of established religion. The first amendment makes this abundantly clear with the words "...free exercise thereof..." The first amendment guarantees freedom "of religion" not from religion. The Founding Fathers were wise in many ways permitting our citizens to be drunk or sober, Christian or Jew, religious or not.
That's true and false. If you remember, the "Founders" didn't put anything in the original Constitution about religion. This isn't that surprising since so many of them were deists - predominantly Masons. They weren't against religion per se; they felt, correctly, that religion could temper public life and would be a good way to keep the rabble in line (sorry, but that was it). It was the people in the state conventions that ratified the Constitution that insisted on the freedoms in the 1st Amendment. One of those is that the state wouldn't interfere with religious practice and, sure enough, it usually doesn't. The one in question here involved the justifiable fear that the state might get behind a particular religion with monetary support and religious tests for holding office with the state, like every other country in the world in those days and, in Europe at least, like most still do today to some extent. What Jefferson was saying in his letter was that the state should keep it's grubby hands off all religions when it came to supporting them, a position strictly consistent with the 1st.
As the Potatoe says, this is a secular country with a lot of religious people in it. Those religious folks have virtually unchallenged rein to do just about anything religious from handling snakes to sacrificing chickens. But giving them control over education or any policy favors from government would be a major mistake and we would be wise to never do it.