This is really hard to have an honest conversation about, because there are so many layers here.
First you've got the team aspect, which means anyone who's a fan will feel like they personally are under attack any time the name is mentioned even as just possibly a teensy bit racist. They'll find any justification to argue that this isn't actually racist and is actually somehow respectful. I don't mind these people so much; team sports make you crazy.
Then you've got the "ZOMG PC run amok" aspect, which means many people will dismiss this as possibly offensive out of hand simply because they feel like it's a victory in some broader battle against the oppressive forces of political correctness. These people seem much more prevalent in this thread than usual for this kind of topic; I'm going to just go ahead and blame Kotaku.
Then you've got social justice warriors, who are sort of the inverse of the "PC run amok" people. These are the people who actually do get off on being offended by shit, and will max out their rage meter no matter the level of the offense. They're far less prevalent than "PC run amok" peeps like to imagine (maxing out the rage meter tends to get you banned from GAF), but they do exist.
And if you can get past all these layers of nonsense, you get to the actual conversation. Is "redskin" an offensive term for American Indians?
My personal take: I've always understood it to be a slur (and not merely in the context of the sports team), and I would certainly never consider using it to refer to American Indians. If I heard someone use it, I wouldn't feel like it was on the same level as some of the racial slurs discussed in this thread, but it would take me aback a little. It's rude, maybe on the level of talking about slanty-eyed Asians.
As far as the sports team, it sounds like many American Indians don't mind the name (though I'd like to see the poll). That's actually quite different from what I expected, and makes me somewhat less annoyed at the owner of the team. Still, I think as a general rule of thumb it's probably best not to name your team after a rude word for a group of people. So it probably ought to be changed anyway. It won't be, because of what I discussed above--the team-sports aspect is mixing with the "PC run amok" aspect which results in a lot of support for keeping the name.
I also want to briefly mention that if you're one of the "PC run amok" people, you should take a moment to pause and consider why you feel that way. Is political correctness
actually ruining our society? Or are you just upset because you feel like internet bloggers are unreasonably attacking your favorite hobby? And please do remember to judge cases on an individual basis, rather than categorizing things as "PC therefore bad" or "un-PC therefore good." And yes, that also applies to anyone who does the inverse.