Banning Rubber Bullets Act of 2020 This bill prohibits the use of nonlethal rounds (e.g., rubber or plastic bullets) by federal law enforcement officers for crowd control or in response to passive resistance and provides that an individual injured by the use of these rounds may bring a civil action. It also discourages the use of nonlethal rounds by state and local law enforcement officers by requiring similar prohibitions as a condition of receiving certain federal funding for crime prevention.