When I first saw Airplane! back in the early 80s, I knew by the first scene with Oveur and the kid that we'd get some gags, but I didn't think it was be anything like this. It was rather shocking. As I understand, as Graves was saying to the kid, "You ever seen a grown man naked?", he was looking around the sound stage for the nearest exit.
Airplane! couldn't be made today in part because it was a scene-for-scene parody of the movie Zero Hour, and airline disaster films are no longer in any sort of vogue as they were in the 70s. But if you're considering the politically incorrect stuff, then yes, because of that as well, this movie wouldn't be made, because nobody's got the guts to do any kind of send up along racial lines. The two black guys speaking "Jive," or the Molumbos, or the little girl saying that she takes her coffee black, like her men, and the Imperial Japanese Officer stabbing himself to commit suicide, along with the Indian dowsing himself with gasoline to immolate himself rather than hear Stryker's stories, would all be cut.
Blazing Saddles could never be made today, for the same reasons.