I'm sure he cheers for Washington, too. I don't know what he'll do at the upcoming game, and I don't care.
I think OP overstated anything by suggesting that it might be a "sin," but on the other hand, most of the ALUFs I know (and living in SLC, going to the U I know a lot) actively cheer against BYU and take every opportunity to tell others how it's a terrible place academically, and otherwise. I don't think they're obligated not to do this, but I do think it's jerky, and I do think it works against the church in the end.
I don't say anybody has to be a fan. I don't says you can't abhor BYU with every fiber of your being and be a good and faithful member. I will say, however, that no one is doing the church any favors when they tear down BYU--especially in front of those who aren't members. (You might argue that you are showing the "diversity of viewpoint" within the church, but I think this is a weak argument.)