Is Facebook viewed as a "common carrier site"? Maybe it should be ... but I don't think it is classified that way. Facebook is not a carrier. It is an over-the-top web site. I suspect it can pretty much do whatever it wants.
So facebook can refuse to bake the cake?
Tell that to someone who prints t-shirts or booklets.
Does facebook “publish” users content for view by those connected to the user’s account as friends or followers?