How does this square up with owners of private property having the ability to determine what they do with that private property? I mean, do these plaintiffs have ownership in whatever social network?

Can spammers sue for being censored? What about bot herders?

I acknowledge that there's some tension in the various rights here, but the USA has rarely mandated that non-common-carriers and non-broadcast media carry particular speech. The old "fairness doctrine" is a notable exception, but we all cheered and waved the flag when that got disposed of.

This looks like a particular political faction having a tantrum about some media not going 100% their way. Back in the Reagan Years, when we all agreed to get rid of things like the fairness doctrine, restrictions on cross-ownership of forms of media and number of markets, one political faction cheered this and everyone else was told cry more, that market forces would take care of things.

Now that markets have shifted, we're seeing the faction that cheered removing barriers crying. I'm having a hard time mustering sympathy, but maybe that's because I'm old.