A partying lifestyle left Wyoming fans at odds with BYU early in the rivalry. Drinking is a religion to some of them.
I think it’s also true that Wyoming football was never the same after the Black 14 fiasco. It never recovered the dominance the Cowboys had in the 60’s when they took LSU toe to toe in the Sugar Bowl. (1968)
Some of the hatred is a bit understandable IMO. The Black 14 decide to wear black armbands in a game against BYU to protest the THEN LDS policy of not allowing blacks to hold the priesthood. Their coach then kicks them off the team for even SUGGESTING to wear the armbands. Wyoming football was never quite the same after this incident. It was a bad look for BYU at the time.
I know BYU and the COJCOLDS have tried very hard to make amends. I think the Black 14 players have forgiven BYU & the Church. The Wyoming fans? (maybe not so much.)