The establishment of a religion by any individual STATE is most definitely NOT hampered in any way by the U.S Constitution.
In fact, many of the several states had established religions well before the formation of the USA, and there were no problems with that. In fact, there were such strictures on representatives; in certain states representatives could NOT be Catholic, right up intil the early 20th century.
The First Amendment reads, and pay VERY close attention to the first word:
CONGRESS shall make no law respecting the establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; orthe right of the people peaceably to assemble, and to petition the Government for redress of grievances.
Nowhere in there does it say that any INDIVIDUAL state can’t alter its laws to prohibit certain religious practices, or even an entire sect.
Yes, it is. Nearly all of the provisions of the Bill of Rights have been incorporated against the states, through the application of the 14th Amendment. The prohibition against the establishment of religion was formally incorporated by the Supreme Court in the 1940s.
The First Amendment also says that Congress shall make no law abridging the freedom of speech. In case you hadn't noticed, states are also Constitutionally prohibited from banning speech, even though that clause originally only applied to the federal Congress.
More about incorporation: http://en.wikipedia.org/wiki/Incorporation_of_the_Bill_of_Rights
Unfortunately, not true any more. Per the 14th (and court cases), the Bill of Rights is incorporated against the states. It's the same reason Chicago cannot ban guns--the 2nd is incorporated against the states.