That's what Alaska bill SB 214, sponsored by state senators Lora Reinbold and Mia Costello would do in part.
I think some restrictions on platforms' deleting posts might be constitutional (see my Social Media Platforms as Common Carriers? article, or these posts excerpted from that article): To quote Justice Breyer (from a dissenting opinion, but on a point which with the majority didn't disagree with, and which other majority opinions endorsed),
Requiring someone to host another person's speech is often a perfectly legitimate thing for the Government to do.
But banning fact checking doesn't just require platforms to host speech on their property—it expressly bars them from engaging in their own speech, since "fact checking" simply means "speech that expresses the platform's view, or the view of someone selected by the platform, about whether some statement is accurate." That violates the platforms' First Amendment rights.
To be sure, some fact checking might be libelous and actionable on those grounds; but the bill would ban all fact checking of "the religious or political speech of a platform user," regardless of whether it's constitutionally protected speech (such as opinion or true statements of fact) or constitutionally unprotected libel.
Thanks to Mike Masnick (Techdirt) for the pointer.
UPDATE: For why I think some properly crafted state statutes (not this one) barring viewpoint discrimination by social media may be consistent with 47 U.S.C. § 230, see this article; I'm also writing an article about when such state statutes may be consistent with the Dormant Commerce Clause, which is a separate question.
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