This isn't about what is, but what should be. What makes Facebook different from FedEx that it should censor messages between willing participants?
Also, I note that you didn't list MasterCard, which has been known to cut perfectly legal businesses loose... and that's a very small industry. You have what? Visa/MasterCard, AMEX and Discover, pretty much.
Because Facebook is not an ISP nor a FedEx. They do not provide a service that ships information.
Now, you can muddy the semantics by saying, "Isn't every website an information shipper?" and even then the answer is still no, that still does not make them a common carrier.
There are what people want Facebook to be, which is some system supporting of their own political views, but the bad faith arguments to project Facebook into being an ISP are not sound.
You didn't answer the question from OP. "What makes Facebook different from FedEx that it should censor messages between willing participants?" Of course Facebook isn't a UPS or a mail carrier, etc, we know that.
Whether Facebook is an ISP or not isn't material to whether it should be a common carrier.
Facebook's social function is as a distributor of broadcast information and carrier of peer-to-peer information for two billion people. Further, network effects mean that Facebook's size makes it a natural monopoly.
There is no shortage of historical evidence that unregulated natural monopolies are bad news for everyone except their owners, and, given that Facebook's function is the distribution of information, the natural path for regulation in a free society is a common carrier designation.
And no, Facebook is a website and app(s), not a common carrier.