The thing about the Simpsons is that it designed the majority of its characters in the early 90s, when cheap stupid racial stereotypes were the norm on television, then times changed and it was stuck with all those characters.
I dunno about that. Even back in the '90s, I always felt that
The Simpsons embraced its ethnic stereotypes a lot more blatantly than most shows -- along with other stereotypes, like its portrayal of the elderly. Of course, it portrayed every character type in an exaggerated and unflattering way -- most professionals were portrayed as incompetent, corrupt, or clueless, and it was something of an equal-opportunity offender, though I felt that its ready embrace of stereotypes was a lazy and cheap way to go for a joke.
It's hard to remember now that
The Simpsons is seen as this cozy, routine, traditional thing, but at the start, it was a very transgressive, boundary-pushing show, infamous for defying the normal standards of good taste on TV. It embraced being controversial and tearing through the envelope. So, yeah, there was plenty of ethnic humor like this back then, but not on commercial TV as a rule, not to the same degree that
The Simpsons took it. The show (along with other FOX shows at the time) broke down the barriers of what was considered polite and acceptable on mainstream TV, for better and for worse.
Heck, if anything,
The Simpsons' ethnic humor was a throwback to the tradition of exaggerated ethnic stereotypes in vaudeville, radio, and classic cartoons -- Chico Marx, Mr. Kitzel, Speedy Gonzalez, etc., not to mention all the minstrel-show black stereotypes of the era. If anything,
The Simpsons was often poking fun at the absurdity of the stereotypes themselves rather than using the stereotypes to be insulting.