Wake me up when people are being arrested for speech, or laws are being passed to restrict free speech. I see neither of these things happening (in the USA) beyond the most extreme cases.
Woody Allen has every right to write a book, but he's not entitled to a publisher publishing it. He could easily self-publish it using any one of dozens of self-publishing platforms, or just put it on the web if he wants. Nobody can really stop him unless there's something civilly actionable in there.
All I see is private companies refusing to provide a platform to content that they don't want to support (often because it offends or just turns off large numbers of customers) or violates their terms. That's not censorship in the legal sense. You aren't entitled to someone else's platform.
Carte blanche access to platforms has never been a thing. Can you imagine walking into a newspaper office in the 1980s and demanding to publish a full page classified ad with any content you want in their newspaper and then screaming "censorship!" and "cancel culture!" when they said no? They'd send you to the psychiatric emergency ward.
The right historically defends the rights of businesses to act freely and would be defending platforms and publishers if it were not far-right content that were being dropped. Since it's far-right content, now the right has suddenly decided that access to large scale platforms is an entitlement that needs to be guaranteed by the state. The right has also done a complete 180 on the anti-trust issue... both only for tech companies that operate content platforms.
It's just so transparently partisan. They wouldn't give a crap if left-wing speech were being deplatformed.
There's one last WTF here. The right was always critical of the sexual revolution going all the way back to the 1950s. This #metoo stuff would be a golden opportunity for conservatives to sling a bit of "we told you so" shade at sexual libertines, pointing out that some sexual taboos may have existed to protect people from sexual predation.
Instead the right sides with accused sex abusers and even pedophiles, but only when the accusers are "libs." It's no longer even remotely about ideas. It's about winning for the sake of winning.