It does no such thing. It is here that the court errs. The First Amendment reads:
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereofWhat the First Amendment actually does is prevent Congress from passing any laws regarding the establishment of religion one way or another. The amendment takes the question of religion out of federal jurisdiction and reserves it to the states.
Correcto! If Arizona wanted to establish a state religion it could. The Feds would have a fit but under the Constitution it would be perfectly legal. The hook of course is that they would threaten to cut off all federal funds. Then of course we would stop paying taxes and then....well you get the idea. God (oops, sorry) but its fun to fantasize.