To the extent that a cancel mob was created by the editorialization of a company (eg promoting specific posts), they can already sue the company for its part - section 230 does not apply to the data that the company itself publishes. And to the extent that the cancel mob organized itself organically, attacking a company for providing a conduit is a direct attack on free speech.

That said if this does pass, we can only hope that the attractive nuisances of webapps will fall out of fashion. User-advocating client software is the real anti-censorship future. Of course what will likely happen is the frog will slowly continue to boil, and the censorship regime will be extended to p2p communications as well.