From an American's POV anything less would probably be considered an additional rudeness.
Every culture makes a public/private distinction and has different social conventions in each.
For example, sarcastic/ironic/cutting humour is mostly a private-space thing in america -- whereas in the UK it's common to both. I'd say this is related to their deep sense that public spaces should be friendly-distant.
For this reason, amongst others, Americans have a reputation for not understanding irony/british sense of humour. It's more that they don't expect it in public places. I'd imagine an American experience of people British people joking at (say,) a funeral is something like a British experience of an American helpline. Vaguely repellent.
It's because it's mixing public/private which crosses intimacy lines. And intimacy is closely related to disgust (eg. someone you dont like kissing you).
PS. I've just had another thought about that. One of the issues we have in the UK at the moment is the importation of a strange kind of political correctness where you mustn't joke about stereotypes etc. (which is a particularly european thing: to joke about each other's culture -- this tends to feel connecting to europeans).
My guess is that because, in America, public spaces are supposed to be friendly-distant (hence why they censor all sorts of words, etc.) we have imported this sense about certain kinds of jokes.
To the American sensibilities a stereotyping joke in a public space is alienating. To a european one, it's a gesture towards intimacy.
I think we're probably going to lose this to American culture. We may have already.
Though still, it's interesting to observe: get a group of europenas of different nationalities together and they bond by joking about sterotypes. Stereotype an american and they think you're being hostile and trash-talking them.