That is true for content publishers. However, if those systems are claimed to be public squares, then there is a right to free speech for citizens of the USA there.

The tech companies cannot have it both ways. They want to be publishers, then take the responsibilities and liabilities of publishers.

https://www.breitbart.com/tech/2018/09/05/jack-dorsey-says-t...

This is a crucial point, IMO. Facebook et al need to decide (or we as a society need to decide) whether they're a public square - in which case they have no business censoring what people choose to say except in cases speech that is clearly illegal - or a content publisher making choices about what to publish and what not.

(In Facebook's case, at least, I'd say that ever since they moved on from the simple chronological "wall" showing posts as submitted, replacing it with a "timeline" where their algorithms - with plenty of input from "sponsors", etc - decide what you'll see, they have chosen to become a content publisher.)

Fine, in the content publisher role they can decide that certain content, or the speech of certain parties, will not be published through their platform.

But then they must also be held responsible for what they do choose to publish - including liability for harmful content such as libel, false advertising, etc.