Facebook banning outside ads for the Ireland abortion referendum comes to mind, as well as the case where a Christian satire site was threatened with a ban for spreading false information because Snopes had fact-checked one of their articles as false. Susan B. Anthony List had a bunch of pro-life ads banned; I think most of them were restored.
https://stream.org/328684-2/ this is a more recent case that follows a familiar pattern: Flagged, rejected appeal, then mysteriously overturned appeal some days later.
Hopefully, you also don't doubt that there are also many examples of Facebook censoring liberal/left/non-Republican whatever stuff, and then overturning on appeal, many times mysteriously so, after initially rejecting the appeal. (This post presents like a dozen examples in the genre of black activists being banned for discussion of racism, such as uploading screenshots of racist and sexist harassment they received. You might also want a warning that these examples are interspersed with the author's strongly opinionated and bellicose comments. https://medium.com/@thedididelgado/mark-zuckerberg-hates-bla... )
Due to their scale and the shittiness of their algorithms and processes at this kind of thing, surely you're not surprised there are tons of examples on every side. (This article documents more examples on all sides, including exemptions for a prominent Republican: https://www.propublica.org/article/facebook-hate-speech-cens... )
What reason do you have to believe these mistakes always seems to hurt conservative causes or that you tend to see conservative stuff get caught, disproportionately more than non-conservative stuff?
If you want to convince me that it's more of a "establishment/fringe" divide than "left/right", that ProPublica piece goes a long way towards making that case.