A grocery store (or other private property) can be forced to host speech, according to common law.
SM platforms are different from newspapers because what is published in a newspaper is so because the newspaper made a choice to publish it. It is the newspaper's speech.
SM platforms are primarily conduits.
Parades make choices about who goes in them. This is their first amendment right, so they can discriminate against gays. They can't be forced to make a choice, akin to a newspaper. The parade organizer is more like a newspaper.
Schools can be forced to host military parades, although they can of course speak out against them.
SM have no space considerations. Forcing a newspaper or tv station to publish something means they can't publish something else which means they lose money on that space, and curtails the owners ability to speak in its own form.
The SC has been very clear on protecting from forced affiliation claims. Plus SM platforms can actively say what they want against opinions. Coerced endorsement.
For newspapers or TV or parades, do editorial decisions occur after the speech has occurred or before? After? That is not what an editor does.
SM platforms have constantly said they aren't the speaker. That it isn't their speech. (Section 230.)
Publishers make a decision to repeat something someone else said. Now they're saying it too. Now you're a publisher.
Common Carrier doctrine dates back before US founding, in common law. It vests states with the power to impose nondiscrimination obligations on communication and transportation providers who hold themselves to serve all members of the public without individualized bargaining. (Telegraph invented in 1830 was the first communications service subjected to Common Carrier at the end of the 19th C. Legislators were concerned private entities that controlled this new tech would use their power to manipulate the flow of info to the public when it served their economic or political self-interest. Western Union (the largest) sometimes refused to carry messages from journalists that competed with its ally AP. The first law required them to receive dispatches to and from any individual on the payment of their usual charges to transmit them with impartiality and good faith. And to transmit them in the order they were received.
Phone companies are privileged by law to filter obscene or harassing expression. Spam calling. And they often do. So phone companies aren't quite required to accept all transmissions.
Public transport companies can kick people off their vehicles. They're forced to accept everybody but can be forced to revoke that.
SM is the dominant means of communication (although not exclusive).
Commerce, friendship, family, speech, persuasion, picketing, pamphleting, concerts, protests. There a public interest in the social media communication.