Federal Permitting Modernization Act of 2021 This bill revises environmental review requirements under the National Environmental Policy Act of 1969 (NEPA) for certain infrastructure projects. Specifically, this bill establishes deadlines for federal agencies to complete the environmental review of such projects. A court may not issue a temporary restraining order or preliminary injunction against an agency or a project sponsor in connection with the review or authorization of an infrastructure project unless the court determines that (1) the environmental review has failed substantially and materially to comply with the requirements of NEPA, and (2) the failure cannot be cured by supplementing the environmental document or other mitigation and monitoring measures.