Beating the Dead Horse
I wouldn't think about this so much if I could just see where the pro-"Redskin" is coming from. I can understand issues based on law, science, law, history, religion or morality, but this has nothing going for it (if you disagree, please explain why).
Many names have no real meaning behind them. The words "perro" and "dog" both mean the same thing and only are used by a convention of language--we have to call them something.
Other names reflect a degree of reality by using sounds ("buzz" reflects the sound a bee makes) or existing images from other words ("catfish"--a fish with whiskers of like a cat). "Anderson High School" is a high school located in Anderson Township. That maintains a sense of logic. Of course, if anyone showed a decent reason, you could argue that the name "Anderson" itself should be changed but I'm not aware of any suggestions to do so. (If Bill Gates offered every resident one million dollars, I'd have no problem with "Gates Township.)
Some names have a sense of poetry behind them-- "The Reading Redskins" would at least have alliteration going for them. "Anderson Redskins" doesn't anything but a basic functional purpose--we have to call them something.
Would anyone care if FDR replaced Hamilton or Wilson replaced Jackson on our money? Would anyone care if the F-16 replaced the bald eagle? The flag is changed everything we add a new state. If someday we have so many states, would people object to replacing the stars entirely? If the flag, something infinitely more important than any sports mascot, can survive multiple changes over the years, couldn't Anderson High School?