I am not easily offended by insults against me. Not because insults aren't a problem, but because the sort of people who hurl insults generally choose topics that don't bother me.
I get very offended when someone, generally a manager at work, implies that I screwed something up (that another worker/the manager in question actually screwed up). I don't need to accept blame for the mistakes of others, I do make plenty of my own.
Around here, if I find someone offensive, it's from a pattern of dismissive or unkind or blatantly misogynist posts. I just use the built in ignore list, and am never surprised when those mushed posts I can't see have gray names by them. I do lump people into a group of "untrainable" after seeing them refuse to take correction - that can be at work, in attitude, or in behavior. I don't dismiss them as "unredeemable" as humans, but I don't have time to interact with them either. Dunno how that categorizes me.