Bring ESA Into the 21st Century Act This bill provides statutory authority for two rules relating to endangered or threatened species. The Fish and Wildlife Service (FWS) and the National Marine Fisheries Service (NMFS) published the rules on August 27, 2019. The first rule revises the interagency consultation process relating to such species and federal actions (i.e., activity authorized, funded, or carried out by federal agencies). Under current law, federal agencies must consult with the FWS and NMFS to review the effects of federal actions on such species or their critical habitats. Among other requirements, the rule establishes alternative consultation mechanisms as well as deadlines for FWS and NMFS to complete consultations. The second rule revises the processes for adding or removing a species to the list of endangered or threatened species and designating critical habitat for such species. Among other requirements, the rule outlines additional circumstances under which critical habitat does not need to be designated for endangered or threatened species.