Beyond that, both Facebook and Twitter receive substantial, unique legal benefits from federal law, further negating the claim that they are free to do whatever they want as private companies. Just as is true of Major League Baseball — which is subject to regulation by Congress as a result of the antitrust exemption they enjoy under the law — these social media companies receive a very valuable and particularized legal benefit in the form of Section 230 of the Communications Decency Act, which shields them from any liability for content published on their platforms, including defamatory material or other legally proscribed communications.

So, if I understand the argument correct, if they are private companies then they should be treated as private companies. If they want to keep their privileges from state then "it's a private company" argument no longer applies to them.