https://www.techdirt.com/articles/20200529/01044044605/no-twitter-fact-checking-president-is-not-evidence-anti-conservative-bias.shtml

I know we've gone through this a bunch already, but there remains no evidence to support the claims of "anti-conservative bias" at major social media platforms. Some people (usually self-claiming conservatives, though they rarely seem to represent actual conservative principles) get really angry about this. But, oddly, none ever seem to present any actual evidence.

Of course, the very underpinnings of the White House's silly and nonsensical executive order regarding social media is that of course there's is anti-conservative bias in the moderation, and it even points to the action that kicked off this entire temper tantrum from the thin-skinned President: they provided a link under his debunked conspiracy theory tweet about mail-in ballots. Many Trump supporters and the executive order itself argue that this kind of fact checking is only done to conservatives: