If we want to be concerned about individual rights, we should at least be somewhat accurate about the definition of the word.
For example, I 'own' my sidewalk, but anyone can protest there. A lot of public space is privately owned, but can still be used for protest.
The internet is the new public square. It can be privately owned, but still forced to recognize the rights of the public.
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.
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.
Here's an example in New York City where the Occupy protests took place: https://nextcity.org/daily/entry/the-21-million-sidewalk-how...
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.
Here's another example in London and Portland: https://nextcity.org/daily/entry/public-space-battle-playing...
https://www.theguardian.com/cities/2017/jul/24/revealed-pseu...
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.
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.
It all comes down to what is popular and unpopular--which is fine in a marketplace. That's exactly how marketplaces are supposed to work.