The PAC-12 conference and other conferences are more than just a sports conference. The schools in the conference also generally share in other things, such as academics. The PAC-12 has some really good academic schools and some of them didn't like BYU from an academics point of view. That, plus the fact that BYU is on the conservative side of the equation and is really religious, it basically killed any chance of the PAC-12 accepting them. They had no problem with playing BYU, and during the independence years, they were one of the more common opponents for BYU (even if you ignore UofU).
There are Big-12 schools that also have issues with BYU. Iowa State's student body leadership complained about accepting BYU into the Big-12 (https://www.amestrib.com/story/news/2021/10/01/iowa-state-student-leaders-complain-big-12-conference-added-byu-without-input-homophobic-policies/5945731001/).
Cursing and swearing at a football game or other sports game is pretty normal throughout the country. A recent famous case occurred in a game between Missouri and Kansas. A student from Missouri had the chance to kick a field goal and win some money. Instead, he lifted up his shirt which revealed "f ku" and then kicked the ball at the Kansas sideline. Both Missouri fans and Kansas fans have applauded him for his action because it showed how important the rivalry was. The problem with BYU is that it almost always brings in religion. Instead of cursing BYU, they curse the Mormons. This also occurs a few times to UofU as well since Utah = Mormons to a lot of people. If the opposing fans just stuck to cursing BYU or the cougars, I doubt there would be any issue. But when the religion comes into play, that is where they cross the lines.