Being in the Air Force I have a bunch of friends with zero BYU background. And they associate BYU with 'Mormons' and zero football history or prestige. (For the record these are fans of Florida St, Ohio St, USC, and Alabama. They also view Utah as a step down from the "relevant" teams, but at least adequate whereas BYU doesn't get that).

I don't think it's due to independence though. You mention a bunch of bad teams that at least have their conference affiliation to help, but those are all P5 conferences. Fresno St or Tulane don't really benefit from being associated with the Mountain West or AAC.

I'm a proponent of BYU joining the AAC, but I don't think they'll get P5 levels of respect until (if?) they are actually a P5