This line of thinking is similar to what happened in the deep south before the civil rights movement. Private businesses didn't want to serve African Americans and the excuse given was its their right to refuse service. Except when all private businesses colluded to deny service to African Americans to enforce an informal segregation.
Eventually the federal government came in and decided race was a protected class.
Obviously the problem isn't as simple as saying Google or anyone else must allow certain groups to use their platforms. Because that compels speech. Which the government also can't do.
Proper legal experts would have to craft it but I think the limit should be somewhere around access and use of the infrastructure. Domain registrars and hosts cannot discriminate. However If Twitter doesn't want someone on their platform I can't see why they shouldn't be allowed to kick them. We just cant allow for those paltform hosts to collude with the infrastructure providers to deplatform others completely.
And I can think of two reasons why from a legal standpoint. 1: most of the internet infrastructure in the US was built with public dollars. Even if its nominally owned by a private ISP, they were paid by the government to build it. Historically the courts have used government funds as a way to enforce legal limits.
2: coordinated deplatforming like what happened with Parlor looks an awful lot like it was an intentional hit to take out a potential competitor to the current online status quo. That should worry everyone really.