Recreation Not Red-Tape Act This bill revises and sets forth provisions related to recreation areas and special recreation permits issued by the Department of the Interior and the Department of Agriculture (USDA) for individual or group use of federal recreational lands and waters. The bill makes permanent certain authorizations, including regarding such permits and the fees charged for them. Interior and USDA shall evaluate the special recreation permitting process and identify opportunities for eliminating duplicative processes, reducing costs, and decreasing processing times; establish categorical exclusions from environmental review requirements for special recreation permits if it would reduce processing times or costs without significantly affecting the human environment; authorize the issuance of temporary permits for new or additional recreational uses of federal lands and waters managed by the Forest Service and the Bureau of Land Management; allow online payment of certain federal passes and fees; develop initiatives to promote private-sector volunteer opportunities; and establish an interagency trail management plan. Permittees issued a special recreation permit may voluntarily and temporarily return one or more of their service days. The bill sets forth requirements for review by USDA of the renewal or adjustment of the allocations for the use of a special recreation permit. Interior and USDA may enter into agreements with states to allow the purchase of federal and state recreation passes in the same transaction. The bill establishes a National Recreation Area System.