relationship with your wife by doing so.

Arguments, and even debates with your in-laws will be at best useless, at worst damaging. Don't directly engage. In the first place, their positions regarding fan bases (and yours some of yours) are not fact-based, but are usually narratives fueled by prejudice; or in other words, massive stereo-typing.

I said "don't directly engage", but that doesn't mean you can't call them out for spouting out crap. However, this has to be done carefully and really with no mal-intent. This is NOT accomplished by arguing a ridiculous statement or accusation, but by simply requiring them to back up their statement statement (but if in doing so, you cause them to become defensive, you won't get anywhere). Most of the time, when the statement is just ridiculous, there are either no facts to back it up, or their stretching a on-off incident, and applying it to all BYU fans.

Also, don't be guilty of doing the same thing, i.e. making stupid, stereotyped accusations (although, if done well, this can be done to make a point about the silliness of their prejudices and accusations).

If you take the high road, your wife will come to form her own conclusions, and as I have seen many times, you'll win her over. Note though, that this will take time--even years.

And if you must, just don't talk football with them. If they press you on the matter, don't be a jerk, or mean, but simply state matter-of-factly that it's not possible when stereotypes and narratives are used rather than actual facts.

I have a few Ute friends and family members. In the past, they did some of the things you mentioned above, and would often quickly bring up in our conversations smack and other garbage. If it was garbage, I didn't respond and let it slide. Now, one of them, still a big Ute fan, only brings up "sporting" rivalry smack, and we have a good relationship.