I never had a problem with the name Cleveland Indians. There are obviously other team mascots named after grouos of people: the Minnesota Vikings, Notre Dame Fighting Irish, Pittsburg Steelers, Nebraska Cornhuskers, and Dallas Cowboys to name a few. Now Chief Wahoo, on the other hand, was a racist caricature.
As for the Redskins, like everyone else I grew up with Washington's football team named that way. It seems weird to call them anything else. But "Redskins" is a racist nickname for Native Americans. It clearly is. This is a case where changing the name is the right thing to do.
Would you like a team to be called the "Fighting Abuelitas" with an elderly Mexican-American looking woman holding a "Matamosca" in a swinging pose hanging in man caves, hats and t-shirts to make profit? Oh hell no!