On one end of the spectrum, it is just fine to hate BYU. It is owned by the church but nothing in the church requires you to like it or, especially, cheer for its athletic programs.
On the other end of the spectrum, John Taylor called BYU "The Lord's University" so I wouldn't go around dissing it too much. Also, it is a huge emphasis (as seen by tithing $$$), so I am sure the church highly invested in its prosperity (even in sports). I tend to think more along these lines.