I don't think you should have to cheer for BYU anymore than you should have to go to the FamilySearch library every week (another great missionary tool). I'm not saying BYU athletics are not worth cheering for. But not everyone in the church needs to be a BYU fan.
However, if people endorse lies about BYU, the honor code, tithing money, and can't see the good the school does in athletes lives & others, I believe their fandom for other schools is blinding them - because BYU, at it's core, is an institution that tries its hardest to make people more Christlike disciples, imperfect as it may be sometimes.