At least you also said what you really mean, that the sexism is problematic, but far too often I have seen people pretend that their issue with a offensive/bigoted/problematic joke is that it is not funny or cliche^. Let's be honest here, that is not actually what bothers people. We only hear those objections when there is something else wrong with the joke; nobody objects to non-offensive unfunny jokes. Groan perhaps, but not object.
^ Usually this manifests as something like "it's not even that it is offensive, the joke is just _lazy_"