I haven't watched many new episodes of The Simpsons, and I don't know if they have a lot left in the tank, but perhaps a more sensitive approach will be used with the character. Hank Azaria seems to be sympathetic.
There's a conversation about this in one of the earlier season DVD commentary tracks, they admit that the initial conception of Apu is genuinely stereotypical, but that they've gone on and added depth and growth to the character throughout the years and as such he isn't just a one-note stereotype.
Originally posted by It's FalseThe Simpsons? Filled with stereotypes?
There is a larger backstory from other seasons that might be mildly useful to you at some point, but as far as things you've missed in the first several hours, here are some things to note: Chloe is a holdover from previous seasons.