Marine Mammal Climate Change Protection Act This bill updates the Marine Mammal Protection Act of 1972 to address the effects of climate change, including by establishing a program to monitor the adverse impacts of climate change on marine animals and requiring the National Oceanic and Atmospheric Administration and the U.S. Fish and Wildlife Service to create a process to list and promote the conservation marine mammal species and population stocks in waters under U.S. jurisdiction for which climate change has more than a remote possibility of resulting in a decline in population, impeding population recovery, or reducing carrying capacity.