The "oh my god oh my god I'm being harmed help you're hurting me" crap is a game they're playing to parlay into their own career of outrage. A few hits and they're made. "How dare you!" and so on.
Apologizing won't make them back off and it won't bring any friends. In So You've Been Publicly Shamed by Jon Ronson, none of the publicly shamed people who apologized found peace. It's because there's none there. The one who was unaffected just acted blissfully unaffected and he was.
People are ultimately unhappy for a different reason. If you check their history they'll post about loneliness, SSRIs, therapists, and how the world is shit. 80% of Americans are happy. You're going to listen to the few who couldn't find their way there?
No. Never apologize.