I see where we differ now: I've experienced that when you are being barraged with mud, some will usually stick, with the exception of maybe groups of close friends.
As such, I don't mean that you are the one who takes the bait, but other members of the group. Bikeshedding is so popular it even has a special name, and it affects the performance of the group relative to the original goal even if you're not the one who took the bait.
So while I agree that baiting/insulting it's not something to be offended about, I think the response should be effectively the same as if it was.
> communication that's intended to falsely undermine your reputation
If a claim is false, that's the most damning thing that can be said about it. Whether it's "offensive" (or whether you're offended) or not is irrelevant.