Depends on the policy. Obviously harassing or obscene speech is one thing and even the government is free to restrict it in certain ways (eg. you're not allowed to scream obscenities in public.) Viewpoint-based discrimination is given much more scrutiny, however, and there's a good argument that that's what Twitter et. al are engaging in. Which is less like "throwing unruly patrons out" and more like "calling people whose ideas you dislike unruly and then throwing them out", which is obviously discriminatory.

Only if the barkeep walks past a hundred other patrons at least as unruly as that one patron is, and the barkeep's history suggest he's spending most of his time focusing on the unruly patrons that he disagrees with politically. All while his policies and public statements claim otherwise.