The show has avoided black ones and Jewish ones, but that's about it. Yeah, there's Krusty's occasional jokes about Judaism, but he's not a Jewish stereotype.
I do think that racial/ethnic stereotypes aren't generally good things to make comedy about, but I also do think that they can be used appropriately for humor in some circumstances.
The guy who was at the forefront of the "get Apu" movement is an Indian and in his own words, when asked about Groundskeeper Willie: "Well, I donít know that many Scottish people in America. I know a lot more brown kids. Thereís a personal impact." So, he's not even looking at the thing holistically, he's just upset because of personal impact. Great.
The "problem" I guess is that Indians are in that middle ground in America right now - most of the first generation Indian immigrants are still alive, but their kids are in their 20s - 40s and Apu doesn't represent them. Yet, Indians are still minority enough and new enough that Apu doesn't come off as an obvious intentional stereotype to white people, as characters like Bumble Bee Man and Luigi do. It might be possible to make Apu even funnier by playing into this and making him even more of a stereotype, although they would have to have at least one other Americanized Indian character to be a foil.