A sincere apology implies that one truly feels bad about their behavior in some way. If someone truly feels bad about something that has public visibility, they should apologize for that for their own benefit, regardless if the other party accepts it.
Whats the benefit though?
I'm talking in the abstract, not about this man.
https://twitter.com/marcatracy/status/1357806202277797889/ph...
I obviously don't know you or the specifics of your disagreements, but I think you should be forgiving of yourself.
You can apologize AND simultaneously it can be true that such other person is also a jerk who purposefully gets offended by stupid things and takes everyone out of context for their own benefit who leads a march to cancel you.
If your jokes are frequently poorly received by her then I would consider telling them to other people. Some jokes can be told to anyone but many have a limited audience.