I think that's largely because people see so many examples of their taxes getting spent on things they either never benefit from, are politically/morally aligned against, or its flat-out stolen....so not also putting public money towards professional sports just frustrates them even if it's not the ideal way to use those funds.
Quite honestly, if the worst thing a politician would do is not advocate using taxpayer $$ to help a team build a new playground stadium complex and see them leave the state, they'd get my vote regardless of their party. I'm probably too jaded currently living in MN, though...