The only thing I find disturbing about Animal Sports is the fact that half the contestants pump modifying drugs into their pets for improved performance. They like to treat it like a Football game (which I suppose is reasonable since they make money), but for use on ANIMALS? I think that's a little extreme.
As for the rest of the sports, I don't really think It has a negative impact on the minds of the animals. They seem to enjoy it even though a lot of other people portray it as 'demeaning' or 'unethical'.