People should not be allowed to communicate certain things which lead to harm to other people, no. I don't understand why this gets turned into "people not be allowed to communicate" (implying "at all"?).
If we think that Facebook should decide what's permissible, then that's US culture being the global nanny. If we let the local government decide what's permissible, then you better watch out because every single genocide in history has involved demonizing the victims as the real danger (so, their speech would be pointed at as "harmful" and banned, the perpetrators would be painted as organizing a just revolution). The worst genocides were conducted with state support, and wouldn't be stopped if local national governments were moderating Facebook. Forming a special panel to decide which groups deserve to get their message out seems like a very dangerous and poorly motivated concentration of power. I can't think of any other ways to decide which speech is dangerous and ban it, therefore I conclude we're stuck with not doing it.
Facebook shows you from the feeds of your "friends" whatever the company decided. Probably based on some algorithms, but it could be millions of cats rolling over the keyboards for it's not public what Facebook really does.
Third parties analyze and weaponize this behavior for many things from comercial interests, to justifying murder, to incitement to violence.
Facebook needs to be held responsible for its algorithms. Somehow. Stupid autonomous car makers will eventually be held accountable for their algorithms too. It's not like they can put some crap in their EULA and be done with it.
PS: Add to it that Facebook is the internet in some places. It's not just one of the websites.
Many people today wish we had a more open world, myself among them. Do you know we didn't used to even have passports? There was no 'schengen zone.' You could freely travel between nations as a human. But as a "temporary war measure" passports began to be required in WW1. And once governments had that new level of power and control, they of course not only did not relinquish it but expanded it magnitudes over. In the US income tax was another "temporary war measure." Government is not your enemy, but it is also not your friend. Beware of the implications of granting power to an authority who does not, or at some time will not, necessarily have your best interests in mind.
People should be allowed to communicate period.
People should not be allowed to harm other people.
A recent example of this are the ability for conspiracy theorists to communicate news stories after these mass shootings that these attacks were staged or the victims are "Fake". This further pushes harmful propaganda that there is not a real threat to students in schools, and the "third party" children are the ones who suffer from this communication.