the legally correct way to have this discussion is to frame it around property rights, and extend concepts of speech that exist in real life into the digital world. it's not as difficult as you might think, except that there's a piece missing - we don't have any publicly owned spaces on the internet. in real life, it is the public square that protests take place in for the precise reason that nobody can clear them out - and we have constitutional rights that ensure nobody can clear them out. this just doesn't currently exist on the internet.
further, having the backbone of the internet run by private companies is a lot like having privately owned roads - it's not sustainable in the long run. the actual internet is of course run by the military; in the long run, it's inevitable that this will be maintained as a part of municipal, regional and national infrastructure. i've long argued for the nationalization of transmission lines and dns servers - and, yes, that means the cops can pull you over if you're drunk, but there should be constitutional protections that prevent them from stopping you from marching down the street. having all of the streets in private hands is a kind of technological feudalism. it may perhaps be when they abolish net neutrality and start charging tolls that we stand up and reclaim the lines.
WHOSE BROADBAND SPECTRUM?
the internet itself is then arranged into sites that exist on privately owned servers. the owners of those sites rent space on these privately owned servers, which is like a business renting space in a commercial complex. of course, some businesses own their own buildings, too. when you go to the forum on the site, it is like entering into a coffee shop or bar and chatting with the people in it.
so, who is going to throw the patron out? the owner of the shop/site - entirely at their discretion. that doesn't need to change, much.
and, who is going to evict the tenant? the owner of the property - in accordance with existing law. this law needs to be written, but my analogy should make it clear how it should be written.
the missing piece is that space for public expression, which is protected by constitutional rights. it's up to people to agitate for it and then keep it truly free....
...but you can't be arguing that you have the right to go on to a private server and say whatever you want, then accuse a private business of a speech violation. that's like walking into a bank, taking a shit on the counter and claiming it's protected - then arguing that the bank is not upholding the constitution. it's completely incoherent.
what should happen here, then? well, the government should be policing the roads. they would need to declare the site an unlawful assembly. and, the site would have access to due process.
http://www.cbc.ca/news/technology/charlottesville-neo-nazis-white-supremacists-tech-hate-1.4253406