the 1st amendment restricts government power.
the Supreme Court has long held that the restrictions apply to all government actions, whether they're committed against citizens or non-citizens.
so, yes.
But this bullshit whereby the government, or through cutouts like NGOs, flags speech they don't like and facebook takes it down or blocks it... that's a bit of a twist.
There is some caselaw holding that private actors - when filling government functions - can't do things the government can't otherwise do.
There aren't yet any "strange bedfellows" emerging here... the appropriate action would be either to break facebook up into smaller pieces so that one entity doesn't privatize & monopolize so much of our virtual "public space," or nationalize it as our national social media platform. If the latter happens, the government can't ban anyone from sharing opinions they don't like on it!
But either action is government taking from a private corporation, and therefore "bad"