Hi All.
Here in England, we have larger religious minorities than you do in Texas, and also UGLE has many overseas Lodges in non-Christian countries, so we've had a lot of experience on this issue. Maybe our practices are an interesting comparison.
Our rule is that the Bible is always on the altar regardless, but also we may have other Books on the altar as appropriate for the faith(s) of those present (although this isn't obligatory except during Degrees). When we have other Books, they're placed alongside the Bible, not one on top of another because that's likely to offend someone. In some of our Asian Lodges (e.g. in India and Singapore) where there are usually several religions in the same Lodge, we'll commonly have half a dozen Books open on the altar throughout the meeting. The Koran is treated differently (wouldn't you just know it, eh?): in accordance with Islamic custom, the Koran is not to be opened or closed by Officers who might not by Moslems, so it is covered with a cloth for "closed" and uncovered (but still actually closed) for "open", and is only actually opened by a Moslem Candidate for his Obligation. (For all other faiths, the relevant Book is opened and closed in the same way as the Bible.)
Although you permit Candidates of other faiths to take the Obligations on their own Book, we positively require it. This is for exactly the reason that Bro. Nate mentioned above: so that we can see that his Obligation is definitely binding upon his conscience.
When Obligating a non-Christian Candidate, we usually place an additional S&C on his own Book, but leave the usual S&C on the Bible as well. When the Master is of a non-Christian faith, we'll often have a S&C on the Book of the Master's faith. These two points are customs, however, not rigid rules. (An interesting variation elsewhere is in Israel, where they usually have Jews and Moslems and Christians at every meeting - in Israel, they use one huge S&C which covers all three Books at once.)
UGLE requires prospective Candidates to believe in "the G.A.O.T.U. and His revealed will", and in practice "His revealed will" means the divine authority of the Scriptures - but by that we mean the Scriptures of his own religion, whichever it is.
An interesting difference is that GLTX also requires belief in the immortality of the soul, but UGLE doesn't require that. Obviously that makes no difference in most cases because most major religions do involve immortality of the soul, but very occasionally it might mean than we'd accept a Candidate whom you wouldn't accept.
T & F,
Huw