I used to feel the way you did, until I had a conversation with a native American. The way he described it changed my mind. They consider it to be the same as having a team called the "n-words", the kikes, or whatever. The "redskin" name makes them feel like they are being made to be inferior to others, which isn't the case.
So my question is this: Do you want to make a population of good Americans feel inferior or insulted, or do you want to simply change the name of a team in a silly game? Put that way, I'm not sure why you'd be OK with insulting fellow Americans.