A lot of your points are valid, but like the other guy said, the same things you say about BYU can be said about other schools. USU fans think their basketball team is better than they really are. Utah fans think their football program is better than it is (no way were they the best team in the Nation 2 years ago, they were arguably 2nd in the conference behind TCU. They got outplayed by them but luckily won the game).
The worst thing about it is when LDS people hate BYU and religion is part of the reason that they hate them. I don't know if getting in to school has anything to do with it or not but LDS members that make fun of BYU and talk about the "Zoobies" are ridiculous. I agree that religion shouldn't be part of sports, so don't make it about that. Yes, BYU fans are to blame just as much as USU fans and Utah fans with regards to this.
For the record, I went to USU as well and like you never considered going to school at BYU. I liked their basketball team at first, but lost interest because of their fans infatuation with hating BYU. For the record, if you're down by 4 touchdowns and make BYU punt, that's not something to go crazy about. And if you win your home games against BYU basketball, but lose the road games, that pretty much makes the teams even and isn't something to brag about (Each has won a road game over the last 10 years and BYU won the Neutral court game).