Stop the Censorship Act of 2020 This bill modifies a social media company's immunity from liability for screening and blocking offensive content on its platform. Under current law, the immunity applies for action taken to restrict content that is obscene, lewd, lascivious, filthy, excessively violent, harassing, or otherwise objectionable. The bill eliminates immunity for restricting content that is otherwise objectionable and applies such immunity when a company restricts content that is unlawful or that promotes violence or terrorism. Under current law, such immunity also applies to actions taken to enable or make available the technical means to restrict access to such content. The bill applies this immunity to actions taken that provide users with the option to restrict access to any material, regardless of whether such material is constitutionally protected.