Greer is a member of the board of directors of Project Chimps, a sanctuary for former research chimpanzees funded in large part by the Humane Society of the United States. In 2020, Greer became embroiled in a controversy in which animal advocacy groups asked that the Board of Directors of Project Chimps drop a lawsuit against former chimpanzee caregivers who publicly exposed animal welfare infractions at the sanctuary. On July 25, 2020, Project Chimps dropped its lawsuit but the controversy and claims of mismanagement have continued.