Everybody knows that it would anger ALUFs and other BYU haters, but another reason that no one seems to be talking about is simply that not everyone cares about sports. There are many members who are completely apathetic about sports; not just BYU sports but sports in general. They don't care, they don't see the value in it and they definitely would not want their tithing money funding it. My in laws fit in this category. I don't think they've ever sat down to watch an organized sporting event in their lives. They just don't get sports.
Hard to believe but it's true. Not everyone cares about sports. I just think if the Church started subsidizing BYU sports with tithing money, then there would be a huge outcry among the general membership in the Church from those who don't care or even think sports is a waste of time or just a trivial pursuit. It would be hard to convince these members that BYU football is a missionary tool.
Anyway, just my .02 on the matter. Personally, I would be fine if the Church helped fund BYU sports with tithing money, but of course I'm obviously a big fan and therefore biased.