The "fat dumb clueless guy" isn't a racial stereotype of whites; it's just a trope that just happens to depict a white guy in this case. Trailer parks or the toothless hillbilly are stereotypes of whites, but not the ones you mentioned.
For all of Apu's "morally upstanding" traits, he's still a stereotype of mid-east or south-Asian people running a convenience store. I ...[text shortened]... ing people. There are plenty of other ways to be entertained that don't involve disparaging others.
I agree with you that white guys have it fairly easy when it comes to stereotyping. I suppose the group is just too large for that.
Still, there exist plenty of "white-ish" stereotypes. The humourless German, the dentally challenged Englishman, the stingy Dutchman. Think I feel even remotely upset because of the phrase "going Dutch"? Hell nah.
We need to be able to laugh at each other and ourselves, and stereotyping to some degree is an important part of that.
Erasing everything that might possibly offend somebody is a terrible way forward.
Are we going to have all South Park episodes burned because of their frequent Jew jokes? What about Family Guy. More Jew jokes than cut-aways in that show.
What about the Scotsman Groundskeeper Willy from The Simpsons? How close would you say we are to somebody demanding to remove him because of stereotyping?
How about jokes about dumb blondes? And mother-in-laws? Is society evolving in such a way that those jokes will soon be banned? Will humour on tv soon have the bite of "Growing Pains", devoid of any kind of edgy-ness, lest we might offend someone?
And going back to Apu, while he is a stereotype, he is based to a degree on reality, which is what stereotypes often are. I suppose we should look away from reality, just like we shouldn't see a person's skin colour.
From now on, there are no longer "south-Asian people running a convenience store".