Does Conservative 'Bias' And 'Censorship' Exist On Social Media Platforms?

In right-wing media discussions about social media, the popular narrative is that conservatives are subject to both bias and even "censorship" on prominent social media sites like Facebook and Twitter. Is there evidence that these platforms are "anti-conservative"? How can platforms better balance efforts to prevent the spread of misinformation and other unsafe content without provoking allegations that that they are infringing on users' rights?