Never apologize, mock the ones who are trying to cancel you.
If they manage to convince your employer to fire you, sue.
If a media outlet publishes a hit piece on you, sue.
Contact online content creators who make a living off of criticizing cancel culture (Shapiro, Crowder, Tim Pool, Sargon etc.) and get them to talk about you, make your story viral.
If you manage to go viral, become active on social media and monetize your situation - sell merch related to what you're going through, start a crowdfunding campaign, advertise your content if you create any, make as much money on this as possible.
You ignore them, never apologize and you make sure your community is there for you, not you there for them. They have no power if you remember these three things.
Honestly, think of internet cancel culture no differently than you would middle school bullies or an abusive spouse, because they use all the same tactics.
No matter how much you want to, you're never going to actually "win" a battle against bullies or abusive spouses, because any interaction is just playing their game and furthering the drama. The only real solution in either of these cases is to leave the environment and render them irrelevant in your life. Like others have said, don't apologize. Apologizing is reinfoircing the idea that you're playing their game. If anything, they can get an "I'm sorry you feel that way", and then you leave.
In the case of cancel culture, that means not socializing with these dipshits to begin with or at the very least, keeping your encounters with them as limited as possible. If you have to have any contact with them online, do it in a way that's anonymous so they can't bother you in real life. In real life, keep your professional life separate from your personal life. One of the biggest risks for encountering cancel culture is combining your internet life, personal life, and professional life into one big social media blob.
If this is infecting your workplace, you should probably start looking for a new job or even consider changing careers. Being a grown adult and trying to work around people who act like a bunch of middle schoolers is not a healthy environment in any context, and a red flag that you need to get the fuck out of there to protect your own sanity.
Sadly, you're going to have to accept that some of your hobbies are contaminated and you'll never be able to really participate in the social aspect of them without encountering these crazy bastards. So it might be a good idea to just come to terms with enjoying stuff on your own for your own sake, or pursuing new hobbies in an entirely different direction.
2 words: Double down.
They try to get you because you made a racist joke? Tell more racist jokes.
They tell you you're sexist? Make fun of women and feminism.
Never back down, always double down.