If a firm’s core business is disseminating others’ speech, then that should weaken, not strengthen, the firm’s argument that it has a First Amendment right to censor that speech. In PruneYard, for example, the shopping mall was open to the public—but for the purpose of shopping, not sharing expression. So it was perhaps tenuous for the State to use the public nature of the mall to justify a speech-hosting requirement. Cf. PruneYard, 447 U.S. at 95 (White, J., concurring in part) (noting that California’s hosting requirement involved communication “about subjects having no connection with the shopping centers’ business”). But here, the Platforms are open to the public for the specific purpose of disseminating the public’s speech. It’s rather odd to say that a business has more rights to discriminate when it’s in the speech business than when it’s in some altogether non-speech business (like shopping or legal education).
A point a lot of commenters here seem to be missing is that it would be perfectly legal under the law to ban all discussion of politics, regardless of viewpoint. The law just says that if you're a site with more than 50 million users, you cannot dictate which political parties your users are allowed to write favorably about and ban users for having opposing viewpoints.
[0] https://www.ca5.uscourts.gov/opinions/pub/21/21-51178-CV1.pd... (PDF)