I'm an alum of Central Michigan University, who's nickname is the Chippewas; they have a good relationship with the Ojibwe/Chippewa tribe whose reservation is just off campus. When the NCAA tried to ban Native-American nicknames, CMU got a waiver after the real Chips next door said they were cool with the nickname. If I recall correctly, the Seminole tribe similarly vouched for Florida State's nickname.
The Washington Redskins are in the news not for RG3's rehab but for another round of protest by Native American activists. I'm not sure if name has quite the pejoritive nature that they attribute to it, equating it to "the N-word." Considering that a fairly culturally sensitive guy who refrains from such put-downs is comfortable using it either means I have a blind spot or, to borrow from Inigo Montoya, that the word doesn't mean what the protesters think it means to modern Americans.
I literally can't recall the last time I heard "redskin" out of the context of the NFL team. Word associate that and I get "the Hawgs" and "Counter-Trey" with "RG3" coming hard on the outside.
Here's Commissioner Goodell's take-
"The Washington Redskins name has thus from its origin represented a positive meaning distinct from any disparagement that could be viewed in some other context," Goodell writes in the letter. "For the team's millions of fans and customers, who represent one of America's most ethnically and geographically diverse fan bases, the name is a unifying force that stands for strength, courage, pride and respect."
Some folks might feel dissed by the nickname, but it's not intended that way. Pacifists might be insulted by the Patriots and an atheist might object to the Saints and Padres, but those aren't going anywhere, either.