Unless it was an obvious thing, like a person I know to be Jewish asking me not to use the term "nazi", I'd ask why, and then make a decision. In the end, unless I had a really good reason for using that particular phrase, I'd most probably remove it because I think that in such a case, it's not a sacrifice to avoid using upsetting language when politely asked to. Otherwise I'd politely refuse and explain my reasoning.

ETA: I would apologise for upsetting them.