Accountability for Online Firearms Marketplaces Act of 2021 This bill removes the federal liability protection that a provider of an interactive computer service (e.g., a social media company) receives for content provided by third parties if the provider operates an online firearms marketplace. Online firearms marketplace refers to an interactive computer service that (1) facilitates firearm-related transactions, (2) advertises or otherwise makes available proposals for transferring firearms, or (3) makes digital instructions for programming a three-dimensional printer to make a firearm.