Twitter etc. are private entities. I don't think they could be sued for "political bias" any more than the NY Times, MSNBC, Fox News, Mother Jones, National Review, etc. Gawker was sued for publishing private sex tapes. And the DOJ doesn't sue anybody for political bias, and it wouldn't have anything to say about a civil suit by one private party against another.
The real issue is that if the media companies lose their identity as an analog of the phone company, they would be responsible for everything that appears on their sites, just as the NYT is. Anybody who is offended or aggrieved by anything anybody posted would be able to sue Twitter, not the poster, for libel, invasion of privacy and whatever other grounds their lawyers could come up with. In effect, Twitter, Facebook etc. would become publishers, legally liable for everything they publish. The other side is that if Congress tries to change the laws, court cases would go on for years, maybe decades. It took 10 years for the DOJ to break up Bell.
I think Jack Dorsey ought to call out Trump by banning him and all of his enablers and even the word "Trump" from his site. Nothing Trump could do could take effect before the election. I bet Orange Man would change his tune.