Increasing Access and Multiple Use Act of 2020 This bill revises permit requirements under the Endangered Species Act of 1973 (ESA). It prohibits the Department of the Interior from requiring a permit holder, without the consent of the holder, to adopt any new minimization, mitigation, or other measure for any species adequately covered by the permit during its term, except to meet circumstances that have changed subsequent to the issuance of the permit. The bill provides that (1) a critical habitat designation or listing of a species under the ESA shall not result in a net loss of acreage, permits, or leases within grazing allotments or other multiple use activities; and (2) the presence of a critical habitat or a species listed under the ESA shall not result in the denial of any federal permit, lease, or expansion of multiple use activities based on the presence of the species or habitat. This bill requires federal public land management officials to facilitate the use of, and access to, federal public lands for fishing, sport hunting, and recreational shooting with specified exceptions. The bill prohibits Interior and the Department of Agriculture (USDA) from establishing policies or regulations that (1) restrict hunting or recreational fishing on lands within the National Forest System or Wildlife Refuge System that are otherwise open to those activities; or (2) restrict public access to public lands under certain conditions. Interior and USDA must make vacant grazing allotments available to a holder of a grazing permit or lease if it is determined that the land covered by such permit or lease are unusable because of a natural disaster, court-issued injunction, or a conflict with wildlife.