Are the two clauses not separated by a comma? As stated above, “Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof”, the or which separates them makes them mutually exclusive.
Imagine if you will that there were no Free Exercise clause. Even though Congress couldn’t establish a religion, it could tell you what faith you were allowed to practice. Conversely, if there were no Establishment clause, Congress could say that we’re all Muslims, but you can practice whatever you want.
Saddam Hussein was a Sunni Muslim, even though he wasn’t very religious. The official religion of Iraq was Islam as interpreted by Sunni doctrine. The people there, however, were ‘free’ to practice their own religion. What those two clauses do is make it so that Congress can’t create a sort of theocracy.
Where Congress is starting to go awry is that it’s starting to favor one religion over the others, Atheism.