I always used to find it interesting that Carl and Dr Hibbert were characters as opposed to caricatures. My assumption is that at the time, the writers wouldn't have dared using racial stereotypes for them, but weren't worried about Apu.
Incidentally, from what I've read (and what I saw in the documentary on this), people aren't demanding that the character be written out. Hank Azaria has suggested stepping aside to allow an actual Asian actor to fill the role, and has also said that having Asian scriptwriters join the show would make sense.
His first suggestion wouldn't make sense - whatever people think, he is the voice of Apu. Also, people who don't regularly watch the show don't understand that whilst Apu's voice is a bit Amos and Andy-ish, he is a very well-rounded character, whose storylines don't only revolve around the usual tales associated with Indians.
The show is way more gentle in its stereotyping compared to (say) American Dad and Family Guy.