The mascot question has become much more acute since I wrote about it here 7 years ago (Offensive mascots, 11/27/09). The NCAA has imposed penalties on teams with Native American nicknames and mascots, and the pressure on the Washington Redskins has become much greater, including many networks that will not say the name on air.
A new poll highlights the stupidity of the whole effort: Native Americans overwhelmingly don't care. They either aren't offended or actually like the names. Which should be obvious, since team names are taken not to mock a culture, but to hold it up as a symbol of pride.
I doubt this will shame any of the people campaigning against Native American names into minding their own business, because they do not have a normal sense of shame when it comes to their touchstone issues. You're either right, or you're a racist/fascist/sexist. I don't know what they would say to Native Americans in this case; perhaps they would argue that they just don't understand. In other words, progressives know better what to be sensitive about than the people do themselves.
When this kind of condescension comes from conservatives, progressives call it racism.