Actually a careful reading of the 1st Amendment shows that what it does is take the question of the establishment of religion out of the Federal jurisdiction and reserve it to the states. "Congress shall make no law respecting an establishment of religion..." Congress cannot establish a national church or forbid a state from establishing a local state religion. There were indeed a few state established churches for a number of years after the ratification of the 1st Amendment.
So there could actually be a state that is Muslim if that state’s constitution does not prohibit a state religion?