To me, the main issue is appropriation. Who came up with and is using the nickname? Is it that racial/ethnic group, consciously using it as an expression of pride, and perhaps even thumbing their nose in the eye of others who might use it as a slur against them? Or has it been appropriated by outsiders – usually a bunch of white guys – who think using the nickname of the marginalized group is funny or fierce or cool?
I'm an Irish Catholic and grew up a Notre Dame fan. We always considered Notre Dame an Irish Catholic institution, at least in origin. Therefore we took pride in the "Fighting Irish" nickname.
However if some super WASPy school/sports team – or God forbid, one in England – had decided to call themselves the "Fighting Irish" because they think that Irish people like to get drunk and fight so it's a funny mascot, well, I would not be happy at all.
I wrote for a paper in Lafayette, La., where the University of Louisiana-Lafayette calls itself the Ragin' Cajuns. Again, that was a name taken in pride by an institution founded primarily by a bunch of Cajuns in what's basically the capital of Cajun Land (Lafayette bills itself as the "Hub City of Acadiana"). If some school/sports team in New York or California had dubbed themselves the "Cajuns" because they think the Cajuns talk funny and like to drink, and rolled out a mascot in overalls like the guys from the Boudreaux and Thibodeaux skits (or the guy from The Waterboy), I think the real Cajuns would be none too pleased.
This is why I always find it ridiculous when Redskins fans defend the name by giving an example of some high school on a Native American reservation that calls themselves the Redskins. Exactly! They have a right to call themselves that. You don't.