Well, not minority rule but majority rule with rights for the minority which is sort of what we're talking about here except that it has nothing to do with the government. What we're actually talking about is how an organization behaves and the NCAA is allowed to behave how it chooses if it follow the law; I don't see anything wrong with the NCAA choosing to be respectful of others.
And while mascots are very, very (VERY!) different, the "if it's only a minority" has obviously been argued in many unfortunate situations in this country's past, so obviously at some point minority rights are extremely important. So I'm guessing you don't disagree with minority rights, the only argument we should have is how far those extend.