I'm not sure what the laws are for physical protests. Do mall car parks and similar places on "private" but non-enclosed land have to accommodate public protest? Is that sort of thing what you're talking about?
I'm leaning towards the idea that platforms with no barrier to entry should be treated as public to some degree, while those with a sign-up process more involved than email and password are still treated as private.
No... I'm talking about things like 'privately-owned public space' in cities like San Francisco (so Salesforce park), or city sidewalks.
In most cities, the land owner even in downtown will own the sidewalks, but there is an 'easement' that says it's a public right of way. However, it's a public space, and anyone can protest or say what they want there. Their freedom of speech is protected, even though the land is private. The land is certainly private because the landowner is responsible for upkeep and can generally modify it so long as the sidewalk meets certain requirements.
All this is to say is that we have a model for privately owned public space -- spaces where private interests have certain rights and obligations and ownership but where accomodations for the public must be made.
In San Francisco at least -- only using it because I'm most familiar -- certain buildings are required to have public spaces, and you in general have a right to be in this space for free. There are even some beautiful rooftop decks that are privately owned but have been made public to meet the requirement -- like the deck on one kearny.
If by “it” you mean privately-owned websites, then no, it cannot be forced to do so. That would be a violation of the websites’ owners own freedom of speech. Not to mention their property rights! I thought the right to absolutely control one’s own private property was the most sacrosanct of conservative values?
"Private" property becomes morally murky when you extend an invitation to the general public to use that space. Doubly so when a small handful of these privately-owned websites are responsible for carrying a the vast majority of the of the discourse on the internet.
As it stands, Google+Youtube, Facebook, and Reddit (1st, 2nd, 4th, and 6th most popular websites in the country) currently have the power to ban, or worse, guide, all discussion of any topic they wish, with no accountability whatsoever. That is a frightening amount of power to have, and one that I don't believe the free market is equipped to deal with its abuses.
This latter problem is something I'm legitimately surprised more people are not concerned about. Just because they're using this power to target something you don't like doesn't mean it won't be used for more nefarious purposes in the future.
If we want to be concerned about individual rights, we should at least be somewhat accurate about the definition of the word.