There is nothing wrong with LDS people hating the BYU athletic department, because (as we frequently point out), it is totally incongruous with the mission of the church.
While BYU football may have been positive exposure for the church in the 80's, it isn't anymore.
The number of honor code violations, (many of which are covered up), the double standard for athletes vs. non athletes at BYU, and the embarrassing conduct on and off the field of people who as you said represent the LDS faith, (like Max Hall) go completely against the mission of the church.

I can't wait for the day that the church decides that BYU is a strong enough university on its own to draw great LDS students who want to study there, and that it isn't like other schools where athletics are necessary to recruit students and funds to the university.

I don't know if the church will ever disband athletics at BYU, (Even though I strongly believe they should), but until then, I think that BYU athletics is about as positive of an aspect of the church as other things that have gone the way of the dodo like Orderville and The Nauvoo Bank.