We don't have jurisprudence saying so for websites, because this is new, but it could be argued that a number of websites have reached a sort of monopoly status. Facebook is probably closest, but Twitter and Wikipedia both occupy unique places in society to the point where it's not, just, "go start your own website".
As far as business freedom, remember the gay wedding cake guy? Where were all these "you're not entitled to Twitter's megaphone" people then? On the exact opposite side of the principle, mostly.
I think people having different attitudes regarding the three categories of service is reasonable.