Bronco is the coach, but they cheer for BYU, not for Bronco Mendenhall University. This tying the coach to the university only works when a coach is a legacy guy, which Bronco is not yet, like LaVell was.
Plus, coaches come and go. Just as players come and go. Fans still show up to cheer for BYU in spite of all those changes. It is the nature of the business.
So just because someone might not be a Bronco fan does not mean that they are less of a BYU fan.
But keeping waging your war on BYU fans who have issues with Bronco. They are still BYU fans.