The site actually hosts several "religious books" (try filtering by the "Spirituality" tag -- I've even produced several books on religious topics myself for SE). What it doesn't host are "Religious texts from modern world religions" (what some might call "scriptures," e.g. the Bible or the Quran) which is a much narrower category than "religious books."

As a religious person myself, I actually think this policy is very sensible. Most (nearly all?) religious texts of major world religions were originally written in languages other than English, and so if SE were to try to host those texts the site would have to make an editorial call about which translations of those texts are the "best." That quickly enters very murky theological territory, where one side of a given religion might push for one particular translation, whereas another side would push for another translation.

To give the Bible as an example, Catholics and Orthodox Christians include the deuterocanonical books (e.g. Tobit, Judith, Sirach) in their canons whereas Protestants exclude these. Would the SE version of the Bible include these? Some American fundamentalist Christians claim that the King James Version is the only valid English translation of the Bible, whereas the Revised Version (also available in the public domain) is based on more reliable Greek manuscripts. But some conservative Christians reject the Revised Version and its descendants based on certain theological premises...

Do you catch my drift? IMHO it's very sensible for SE to avoid these sorts of debates entirely by sticking to books where you could argue (with some degree of handwaving) that there really is a "best version" :)

My thought was that many/most religious works are public domain and are already readily available elsewhere.

I'd imagine that if they host one religions books, many more religions will come out of the wood work and demand their books also be included, leading the site to be largely religious texts.