Protecting Federal Workers Act This bill nullifies certain executive orders concerning federal-employee collective bargaining, classifications, and training. Specifically, it rescinds orders and a memorandum that limit the use of unrestricted grants for union activity, specify objectives for agencies to negotiate collective-bargaining agreements and establish the Interagency Labor Relations Working Group, establish principles for the removal and discipline of federal employees and other personnel issues, prohibit government contractors and other entities from conducting specified workplace training related to race or sex, place certain executive agency positions under a new schedule in the excepted service instead of the competitive service, and delegate authority to the Secretary of Defense to exclude the Department of Defense from certain labor-relations requirements.