Earlier quoted context omitted.
It is completely legal for businesses to deny service as long as it's not a protected class. I, as a freelancer, refuse to work with certain "difficult" clients at my sole discretion for example.
As a freelancer, you are usually not working with "the public". A bunch of professions require special licensing to be able to deal with the public (supermarkets included, but even one-man professions like public notaries in some countries), and while there is no similar legislation for internet "places", we can easily establish de-facto public services (which most social networks are). So, if you've got an open shop…
There are, of course, edge cases. For example, a shopping mall is a private space but not in and of itself a retailer. IIRC, they are held to a higher standard than retailers and must have a real reason to deny entry. And then there are the cases of using one reason to deny service when really you want to deny service to a protected class. Those are common lawsuit material.