If your loyal to your school went to BYU etc why be a Utah fan? Unless you follow the crowd, jump on the bandwagon if whoever is winning.
There are other reasons, many like BYU because it’s the church owned school but didn’t go there. Etc.
I don’t personally see your situation with your son as representative of a majority shift to Utah fans. Maybe in dome areas but not overall. We still have more fans on game day at the stadium . Look at TV numbers etc. there are huge amounts of BYU fans. Personally if my son asked me that (he wouldn’t even ask because he knows). I’d say heck yes of. Purse i am!!! Best team on the planet! Blue all the way! Go cougs!! As if the Y gear i wear all the time wasn’t enough. People love BYU! (Except some Utah fans). Who were taught to hate BYU with a passion and at all costs by Meyer and others and carried on by Whitt.
I’d be more inclined to think those razzing your son are from Ute families and taught to hate all things BYU and know your son or his fam are BYU fans so trading him about it. Or just followers of what THEY think is popular.