Property Rights Protection Act of 2020 This bill specifies certain rights for private property owners or lessees. Specifically, the bill prohibits the Department of Agriculture and the Department of the Interior from conditioning the issuance, renewal, amendment, or extension of any land use or occupancy agreement on the transfer of any water right to the United States, or on any impairment of title or interest granted or otherwise recognized under state law, by federal or state judgment, or pursuant to any interstate water compact; or requiring any water user to apply for or acquire a water right in the name of the United States under state law as a condition for the issuance, renewal, or extension of any land use or occupancy agreement. Non-federally owned land and water may not be designated as critical habitat without the written consent of the property owners unless a threatened or endangered species is at risk of extinction without such a designation. The department concerned must pay an owner or lessee 150% of the fair market value of real property and is responsible for all related costs. Interior shall issue a final rule that requires the U.S. Fish and Wildlife Service to follow rules substantially similar to the requirements for the U.S. Geological Survey to obtain permission for certain access to private lands. Furthermore, it shall not be a violation of law to take any animal if it poses a recurring threat to life and property.