They don't have any duty as far as governing the non-profit, but as majority shareholder of the for-profit subsidiary, the non-profit would still have a fiduciary duty to the subsidiary's minority shareholders.
Duties to not dilute them or specifically target them, but majority can absolutely make decisions about executives even if those decisions are perceived as harmful.
That decision does not dispute what you quoted at all. That case is not even about the first amendment, it is based on California’s state constitution. In fact your link makes the exact claim as the one you say is false.
> the federal constitution's First Amendment contains only a negative command to Congress to not abridge the freedom of speech
Touché! But the bit I quoted is something of a non sequitur as this case, like PruneYard, concerns a state law extending additional speech protections into the private sector, so PruneYard does seem relevant, as PruneYard affirmed a state’s ability to do this. Further, it doesn’t seem much rebuttal of this ruling about a state law to argue the First Amendment offers no protection to those censored by Facebook (as the part I quoted was doing). The First Amendment enters the case in terms of whether it protects Facebook from this law, not whether it protects users from censorship corporate censorship.
