The Jazz are Utah's only pro sports team. Fans of the Jazz are not mainly limited to one region of the state, but the entire state as a whole. The Houston example is different because he owns the HOUSTON Rockets, not the Texas Rockets. He is a booster for University of Houston. Being the owner of Houston's pro basketball team, and a donor for their local University is not something that would piss a large number of his fans off... especially since Houston isn't exactly competing with the likes of Texas.

If this guy stays vocal about his support for BYU, it is a virtual guarantee that he will lose some Jazz fans. BYU and Utah compete directly for fans. The Utah Jazz fan base is comprised of fans of both universities. The Utah Jazz are located in Salt Lake City, home of the Utah Utes, not the BYU Cougars. He stands to lose a substantial portion (obviously not the entire fanbase, or even most of it, but a large number of fans nonetheless) if he is vocal about his BYU fandom.

Now, I don't know if the number of fans he would lose is enough for him to tone down his support of BYU, my guess is the difference in his bank account would not be noticeable really, but it could be a headache that he may want to avoid.