Yep, it seems the options are:

- Issue apology and piss off those who agreed with you and those who didn't won't acknowledge the apology

- Don't issue apology and those who agree still agree and those who don't will forget about it/get over it.

You’ve left out the part where apologizing (i.e. appeasing) the mob rewards them with a “win”, reinforcing their behavior.

As a father of a small child, I’ve learned that it’s important not to confer extra attention for acting out, otherwise I am effectively encouraging that behavior. I’ve heard this described as “don’t water weeds”.

The modern mob is nothing more than the collective Id of so many sad, child-like human beings. Don't give in just because it’s easier in the short term. Don’t water the weeds.

Company apologies don't work, they buy time until people stop giving a fuck.

Personal apologies generally don't work if they're anything beyond what is demanded by conversational etiquette, since the people demanding them usually just want an admission of guilt they can hold over you forever as leverage, and anybody who agrees with you will be disappointed.

That works for a company but it won’t work for a person. For a person an apology becomes a tacit admission of guilt and license for further harassment. See Chris Avelone, etc.