Mostly, my feelings about this come down to whether the caricature is funny/entertaining enough to let me blow off the more racial aspects of what's on-screen. I think characters like Miss Chinglish in Black Lagoon, the restaurant owner in South Park, and Amy's parents in Futurama are all hilariously funny despite the fact that they're all gross stereotypes to a degree. I can even identify the exact moment when Amy's parents went from giving me a queasy, "We're going there, are we?" feeling to a "Oh, we're going THERE. Well, that's OK, then" feeling ("I know they Martians because they grammar so bad").
I will also say that I'll give cartoons more of a pass for this sort of thing because of the inherent abstraction in animation. I'm not looking at an Asian person, I'm looking at a drawing of an Asian person, and I think that extra step further away from reality is what makes it easier for me to swallow a lot of the more ridiculous/caricatured elements of their portrayals and the fact that they're all white people affecting thick Asian accents. It's the same rationale why The Simpsons is funny as a cartoon, but doing most of what they do in live-action would make you actively uncomfortable. A live-action actor in yellowface is also an abstraction of an Asian person, but it's not far enough from reality that I can't blow off the fact that I'm looking at a white guy in a lot of (often bad) makeup. It ruins the suspension of disbelief.
While I don't think that anybody's very well served by censoring these cartoons (nothing is so dangerous that it can't even be talked about), I also think that just putting them out there without any context doesn't really help anyone, either. I don't particularly like Charlie Chan movies, but I'm happier that they're on the market than not. I'd like them even more if they put added of the documentaries about portrayals of Asians in Hollywood as bonus features, or even packaged excerpts from Margaret Cho's I'm the One That I Want, which (in addition to being uproariously funny) documents the damage Asian stereotypes in Hollywood did to a real live person a lot more recently than anyone would like to acknowledge. I don't want them to censor Charlie in the Mister Magoo cartoons or anything in the original Charlie Chan and the Chan Clan cartoon, but I also think you can't just throw them out there without SOME kind of acknowledgement that, "This is a historical document and no, it's kinda not cool to do stuff like this any more."
Regarding stuff like Soul Plane or Norbit: I get to say things about Asian people that non-Asian people can't say. Black people get to say things about black people that non-black people can't say. This is no different than the fact that I can fling all kinds of nasty, horrible obscenities at my brother and he can do the same to me, but a stranger doing the same thing to him in my presence is going to get a punch in the nose.
The last thing I have to say is that what bugs me more about topics like the Censored 11 or Song of the South is an attitude I frequently see of, "I'm not offended by this, so nobody else should be either." You kind of don't get to decide that, and all it succeeds in doing is ticking me off more than I would have been otherwise. I understand all the arguments for why I should be flattered by Charlie Chan, but I don't find any of them convincing and just telling me to "get over it" is the most counter-productive counter-argument anywhere ever.