The best example of the "wouldn't be allowed to be made today" is Tropic Thunder.
I think a better example of movies which "wouldn't be allowed today" is probably something like the Hangover, which just mines outdated stereotypes & slurs for laughs. Just a sign of society moving on really (as much as Todd Phillips likes to cry about it, I feel his inability to adapt to the comedy landscape is really just a failure of the imagination). I thought the 21 / 22 Jump Street movie addressed this issue quite well it seems the shift took place sometime between the two releases
But I'm not sure how many things are really outright taboo. For example, I've also heard people say that Heathers couldn't be made today--can't be threatening to blow up a school--but it was actually staged as an off-Broadway musical not all that long ago.
Borat is racist, it's not 'satirical' and that's ok, the world's complicated. It's also ok to hide behind 'satirical' as everyone does, except when you get picky on movies you personally don't think are 'satirical'
Hollywood's inability to deal with kissing is academically interesting. Currently combining sarcasm with the 'correct' actions they are told to follow. It's a dangerous path towards the religious moralism we left behind in the 60's, but perhaps I fear change.
The idea nothing is happening is incorrect.
Blackface being problematic isn't something we just figured out in the last 12 years, and people trying to do something funny with it anyway isn't new either.
I still don't quite get how they managed to get a movie centered around a character in black face made, even though it was obviously a parody.