I could see that to a degree. But that's a different question.
Right now, the First Amendment only covers government action. The Fourth does too. Now, when the government was seeking records, that absolutely should implicate the Fourth Amendment. That should similarly happen with the First if it's the government asking for certain types of speech to be disallowed somewhere.
But the Fourteenth and Nineteenth don't create those employment and public accommodation laws. They, too, only restrict the government. It's laws, like the Civil Rights Act, that put into place the actual protections against discrimination by private actors.
I'm not sure how the constitutionality of requiring Twitter, or Slashdot, or any other platform to let anyone use its services without restriction would come out. I suspect they could readily argue that it violates freedom of association; that they have the right not to be associated with those people, and to kick them off their property. But there might be some success in making "political persuasion" a protected class. Of course, the lawsuits over what exactly falls under that would be nothing if not endless.
But realistically, I think the whole thing is overblown. I saw tons and tons of pro-Trump stuff on social media. Trump himself was certainly never barred from using Twitter, and does so to this day. If Facebook won't even stop flat out lies masquerading as news from being posted, I think they're being pretty permissive.