Last time I saw it, I was struck by sort of the opposite: how much of what COULD be offensive in today's culture is neutered by the warm-hearted nature of the material. Mel Brooks may be an equal-opportunity offender, but his sense of humor about it is oddly cuddly. The only person who the joke is ever really ON is Bialystock himself- Roger DeBris may be a drama queen, and Carmen Ghia an outdated 1950s "nelly" stereotype, but neither one is usually the target of the punch lines. Ulla is WAY less of a bimbo caricature than she was in the original film as well.
It's bawdy humor, but Mel Brooks is of an older, kinder generation of satire. While the jokes in "Book of Mormon," for example, may be much more pointed and satirical today, there's also an element of condemnation and judgment in much of it that you don't find anywhere in Mel Brooks. There's a difference between "Roger DeBris is a swishy kook" and "third-world Africa is messed up."