I tried to give this issue some thought before weighing in because I think it's a little complicated. First and foremost, for anyone who wonders why discussions about religion matter, here is a case in point.
Ron Brown is by no means alone or even a minority voice in the Christian community. In every church I've ever attended regularly--and these range from mega churches to small congregations of less than fifty people--the basic stance on homosexuality, as dictated by the bible, is that homosexuality is a sin. The things Brown says should come as a shock to no one, and what people should quickly internalize is that he really believes this stuff. He thinks he's doing the Lord's work. Many Christians believe homosexuality to be a sin. I repeat, a sin. Someone who 'practices' homosexuality is, by definition, a sinner, and not in the sense that all have fallen short of the alleged glory of God, but a practicing sinner.
While mainstream America and even some aspects of religion have been brought kicking and screaming into the 21st century (and will continue to come along thanks to the country's youth who generally have no patience for bigotry), this is simply a case of civil rights vs. religion. Almost all opposition to the gay rights movement is religious in nature, and flows directly from the so-called logic employed by Mr. Brown. The part where this gets tricky is that Brown has a right to his bigoted religious views. And while it's comforting to see that most sane people condemn his public statements, it doesn't much change the fact that if you're gay and you play running back at Nebraska, so long as Brown is coach, you might have a problem.
I don't know that the university would have grounds to dismiss him for A) claiming to be a football coach at Nebraska (which he is), and B) spouting discrimination at a crowd while not working in his official capacity. The real question is, do the fans of the program want Nebraska to be known the place with the coach who's going to try to share the love of Jesus with gay sinners in the locker room? In the year 2012?
I don't have a great answer to this question.