I also would not mind someone handing out the Koran to those who want one, or any other classical work. A lot of kids who are reluctant readers would try to struggle through Mao, or the Koran, just because they are different, and that would help with the three Rs. Far more would take a Bible and eventually read it than would take any of what I consider the lesser works. I consider that a big win for America.
As for the pervert lobby (NAMBLA, Hillary's "It Takes a Village to Brainwash a Child", etc), I see no inconsistency in banning their filth while permitting classical religious works and other writings of historical importance. As for the question of the 1st Amendment, permitting the distribution of religious literature in school in no way constitutes a state establishment of religion in the sense of the Church of England or the Lutheran Church in Germany. It is a good thing on those rare occasions when the schools stand up for the actual meaning of the First Amendment and explain to our students why the ACLU's anti-freedom message is a dishonest interpretation of our basic rights.
Actually when I was in school we had a section in social studies that discussed religions and we read many excerpts from many different texts. However, that being said, after hearing lots and lots of people on this very site remind me again and again and again that Mormans are a cult and aren’t really Christian, I know that some people are so blinded by their own “rightness” that it wouldn’t stop with just passing out Bibles or Korans to interested students. Further your definition of “filth” would surely be disputed in court which means lot of money coming from school budgets going to lawyers instead of teachers. It’s such an easy thing to just let Bibles be passed out outside of school grounds. I think the consequences of NOT doing this could and most assuredly would be far worse. You have to ask where does it end and it’s not too hard to see where this will end up in a country where anybody can and will sue anybody over anything.