The Nick Bostrom fiasco is instructive: never make public apologies to an outrage machine. If Nick had just ignored whoever it was trying to blackmail him, it would have been on them to assert the importance of a twenty-five year old deliberately provocative email, and things might not have ascended to the point of mild drama. When he tried to "get ahead of things" by issuing an apology, he ceded that the email was in fact socially significant despite its age, and that he did in fact have something to apologize for, and so opened himself up to the Standard Replies that the apology is not genuine, he's secretly evil etc. etc.
Instead, if you are ever put in this situation, just say nothing. Don't try to defend yourself. Definitely don't volunteer for a struggle session.
Treat outrage artists like the police. You do not prevent the police from filing charges against you by driving to the station and attempting to "explain yourself" to detectives, or by writing and publishing a letter explaining how sorry you are. At best you will inflate the airtime of the controversy by responding to it, at worst you'll be creating the controversy in the first place.
The professional class would be PR people. A vaguely remember reading that the firm that handled Biden's sexual assault allegations also did good work for other people.