Root and Stem Project Authorization Act of 2021 This bill authorizes the Forest Service and the Bureau of Land Management (BLM) to enter into a contract or agreement with another entity to conduct a Root and Stem project, which is a stewardship end result contracting project that is proposed prior to completion of the environmental review process under the National Environmental Policy Act of 1969; and satisfies certain requirements specified in this bill, including concerning environmental analysis and review. The Forest Service and the BLM, in coordination with state and local stakeholders, shall identify areas well-suited to conduct Root and Stem projects, and issue requests for proposals for such projects. Root and Stem projects shall be subject to judicial review in the same manner as authorized hazardous fuel reduction projects.