Am I mistaken or Is this not the case? If you are a platform for expression, you have certain freedoms from the consequences of what is posted on your platform, but in exchange, you cannot censor what is published on your platform. Example being a phone company. You can't sue Verizon because you got a death threat from a liberal in a phone call, but then Verizon can't monitor phone calls and cut off conversations that support President TRUMP! (and just to note for the peanut gallery, that's what he will be called the rest of his life, chuckle). If, OTOH, you're a publisher, you have the luxury of censoring viewpoints you don't like, but are then more liable for what your publication expresses. Example being a magazine. They are free to publish articles written by anti-TRUMP! writers, but you can sue them if a liberal writer identifies your neighborhood as being pro-TRUMP! and a deranged liberal sets your house on fire. It seems to me that the big social media companies want the protections of being a platform but the freedom to censor of being a publisher. That needs to be resolved one way or another.
Either way, the First Amendment doesn't enter into it.