Their target market doesn't care. The church is trying to change perceptions that will help new people come in from the outside. BYU doesn't work like that. Their target audience is mostly just LDS people, many of whom go there because of the weird things.
There's no pressure for the admin to act like they care about athletics, because as long as they're not Rutgers-bad in sports, they don't care. The department makes money (that Skylar White is apparently stashing in a storage unit somewhere to rot) and they're not losing. So that's all that matters.
They'll never listen to anyone about change because they'll maintain the "why fix what isn't broken" attitude.