https://en.wikipedia.org/wiki/Pruneyard_Shopping_Center_v._R...
As to how you would implement it, Poland recently had a proposal that if you were banned from a social media website, you can appeal via the government in a certain period of time.
https://news.ycombinator.com/item?id=25736155
I'm not a lawyer, so I might be saying a bunch of nonsense here, but you could categorize the social media into topical (eg. HN is about technology) or "general purpose", off-topic services (Facebook, Youtube). Or just do it by the size of user base. Facebook has like a 2 or 3 billion users, let's not pretend it's the same as a comment section on your blog.
It's just to throw some ideas around, because again, not a lawyer, so I can't come up with a robust policy on the spot and take care of every potential loophole.
The first amendment works now by having clear boundaries between private and public spaces. Public spaces have clear first amendment protections. I can hold a sign on a publicly owned sidewalk (well, public right of way) begging for money or praising 'bong hits for Jesus'. But private spaces do not. I can't do the same thing on your living room. This allows folks to exercise their freedom of association, which is a pretty big part of the first amendment.
Where and how do you draw the line between public and private spaces then in an online context? Should the government be required to host unmoderated and uncensored discussion boards? And how do you keep the unregulated public spaces useful when such spaces are easily overrun by trolls and spammers?