Marine Mammal Research and Response Act of 2021 This bill provides support for efforts to protect marine mammals. Specifically, the bill reauthorizes through FY2026 and generally revises the John H. Prescott Marine Mammal Rescue Assistance Grant Program, including by renaming the program as the John H. Prescott Marine Mammal Rescue and Response Grant Program. The bill also establishes the Joseph R. Geraci Marine Mammal Rescue and Rapid Response Fund for providing emergency financial assistance for certain stranded or entangled marine mammals and otherwise provides support for marine mammals.