>The problem is that companies like Facebook and Twitter are already operating like the public town square.
The operative word in the above sentence is 'like'.
FB and Twitter are not the town square and never have been. They are the platforms of private corporations driven by profit from advertising sales.
And they haven't been shy about explaining exactly what you can and cannot do on their property either (cf. the relevant sites' TOS).
That many people treat them like public squares is a result of those people's ignorance of or misapprehension about the platforms, not any subterfuge on the part of FB or Twitter.
And the only reason they have any influence is because those people gave it to them.
Don't use those platforms and they have no influence over you.
In the United States at least, they have the right to censor whoever and whatever they like. Whether that be Donald J. Trump or, anything concerning puff pastry or even tasty, tasty jelly beans.