The question of race on The Simpsons is interesting if you think about it. There are few minority characters--much fewer than any real city would have. That alone tells you how the show is trying to avoid the subject. Early on, I believe people criticized it for making everyone yellow and homogeneous, forcing the creators to add characters of (another) color.
The few minority characters fall into one of two categories:
Hugely stereotypical: Apu and his family, Groundskeeper Willie, Fat Tony, Bumblebee Man.
Devoid of (traditional) stereotypes: Carl, Dr. Hibbert, Lou.
The show has gone overseas to explore (or is that exploit?) other cultures: China, India, Brazil, France. As far as I know, it's never taken a sustained look at blacks, Latinos, or Asians in the US. It's as if non-white cultures are out there somewhere, foreign and exotic to us Americans. They're something we visit on vacation before returning to our safe white enclave.
Curiously, though, The Simpsons has had several shows featuring Native American themes:
Bart to the Future (2000)
The Bart of War (2003)
Margical History Tour (2004)
Little Big Girl (2007)
There's also "Missionary: Impossible" (2000), which features South Seas "natives" who are perfect analogues for traditional American Indians. And this trend continues in The Simpsons Movie, which features a Native medicine woman in a key role.
What can we conclude from this? That American Indian cultures seems as foreign and exotic as those of China or Brazil to the Simpsons' creators? That American Indian issues are so vital they deserve more time than black, Latino, and Asian issues combined? That Indian gaming has thrust Indians into the spotlight and given them their 15 minutes of fame? Or what, exactly?
I don't know, but I'm keeping my eye on The Simpsons.