In California at least[1] people are able to peacefully exercise their right to free speech in parts of private shopping centers regularly held open to the public. So the shopping center is not able to throw them out.
I agree with this ruling and would like to see it applied Federally and to the digital platforms that allow the public to submit their own content.
Like I said I am OK to remove content or people who are obscene, lewd, lascivious, filthy, excessively violent, harassing. but otherwise if you open your property or the platform to the public, you let them bring their freedom of expression also.
[1]https://en.wikipedia.org/wiki/Pruneyard_Shopping_Center_v._R...