> Under the principles of free speech, it’s more ambiguous.
I don't think it is. The First Amendment gives companies control of what gets posted to the sites they own. And it gives you that control for the sites you own, too.
> First Amendment gives companies control of what gets posted to the sites they own
No, it does not. It prohibits the government from abridging the freedom of speech.
The First Amendment is a particular expression of the broader principle of freedom of speech/expression [1]. If you are in my home and you express a view I dislike, it is completely within my legal rights to ask you to stop speaking or else be asked to leave. I could not at the same time, however, say I stand for free speech.
> that does not give companies and individuals the ability to choose what they host on their sites?
No, it does not. The First Amendment is silent on e.g. ISPs or payment processors blocking a particular site based on its content. Until 1897, it was unestablished whether it restricted the states in any form [1].
Nobody said it’s acceptable. What’s ridiculous is to claim the difference in scale “doesn’t matter.”
> you don't have a right to use privately owned web sites
Under the First Amendment, no. Under the freedom of assembly, no. Under the principles of free speech, it’s more ambiguous.