associated with that religion.
It's true- some of the more liberal academic universities might not be very tolerant of a religion that many view to be socially conservative. I'm sure that that was A factor, but I don't think it's fair to say it was the only factor.
More than ideology- college sports are about MONEY. And I would assume that BYU's brand and national following would make the school very attractive to a lot of conferences. (There are people I don't like or agree with, but if working with them is going to make me richer- game on!)
BUT... the whole "No Sunday" thing is probably a huge deterrent. For football- no problem. But for other sports- it's a huge problem. And I don't think the PAC-12 AD's are going to want to adjust the entire schedule for just one school. Maybe the Big-XII will.