Here's the thing: I don't think cancel culture exists, at least not in the form that is popularly disseminated. I think that cancel culture is one of two things, both of which are lumped together as an evil phenomenon.
Branch one is people rightfully getting called out and shut down for their goddamn idiocy. Justine Sacco is a great example, because she posted a dumb racist joke and then got fired. Why'd she get fired? Well, would you, if you were a person of color, want to work with a stupid person who makes racist joke? Maybe, maybe not. It's a liability for the company. See ya, dipshit. This is not a left thing, though. This tends to be led on Twitter by progressives, liberals, and unaffiliated decent people who are outraged by bigotry.
Branch two is weaponized discourse by the right. They plumb the depths of someone's social media and find shit someone said from years ago, remove context, sometimes even fake stuff, and they try to get people fired. Usually they target public media figures. You rarely see them going after a day-to-day person like a Justine Sacco. You see them go after James Gunn.
There are other, unaffiliated things that aren't part of cancel culture that also happen and they're their own boxes of rocks.
One example would be deplatforming, which the left definitely has done for idiots like Milo Yiannopoulis (as he tweeted here ). Ultimately they weren't even the ones who canceled him--see branch two. But leftists protested him and his tour where he threatened to out trans and undocumented students like a real piece of shit.
Another unrelated example would be targeted harassment. It's lumped in with cancel culture but it seems to be mostly about terrorizing marginalized people in public forums. JK Rowling bitched about being shouted at by trans people when she said horrible stuff, and a small sliver of unaffiliated people took that moment to say fucked up stuff to her about sexual assaulting her, but it would be extremely, extremely disingenuous to say that's representative of the majority of responses she got, let alone members of the trans community.
In short no one can tell me what the fuck cancel culture is, what its consequences are, or anything but it's pretty clear it's just a tired revival of so-called PC culture hysteria to paint reasonably asking neoliberal goons like Bari Weiss to fuck off as some sort of witch hunt.
As much as cancel culture is discussed, I have never heard a suggestion about how to fight it. Is the plan to just convince people to stop criticizing other people? That doesn't seem likely to work. Is it to stop companies from firing people who have been cancelled? They are doing it out of self interest, good luck stopping that. Is it censoring criticism? Surely that would be worse than anything cancel culture could do.
Cancel culture rhetoric is condensed liberal weakness: endless criticism with no solutions offered.
That's literally what most of them seem to want, yes. Or freedom of consequences for their bad ideas.