I wonder if we'll hear the "they're a private company, they can do what they want, it is only censorship if the government does it" routine. I remember about a decade ago when certain parties were so concerned with voices being silenced and "erasure." The same people are now cheering when Facebook, Twitter, and the like shut down certain kinds of speech, with great discretion as to how the "rules" are implemented. Th…
Two things are additional considerations that may change how this sort of action ends up for Zoom:
1. Zoom will be judged in the court of public opinion for their decision to align their moderation of access to their service with the CCP. This is likely a different degree of backlash than you'd see with, say, shutting down the accounts of US-based hate groups.
2. Zoom may come under scrutiny—without concrete evidence—for introspecting the content of communications through its platform that would otherwise be presumed to be private. This is different from Facebook/Twitter etc., for which much of the content that drives moderation decisions is public.
Zoom is not abridging anyone's constitutional right to free speech, nor would they be able to. How they are judged for their specific actions, though, is entirely at the discretion of their user base and public opinion.