Working to Address Recruiting and Retention to Improve Our Readiness Act or the WARRIOR Act This bill addresses the funding of certain Department of Defense (DOD) activities as well as certain personnel and training matters. The bill prohibits the use of federal funds to (1) take into consideration race, ethnicity, color, national origin, or gender of an individual when making a determination regarding a military accession, assignment, selection, or promotion; (2) promote at the service academies, in military training, or in professional military education the theory that individuals, by virtue of race, ethnicity, color, or national origin, bear collective responsibility for actions committed in the past by individuals of such race, ethnicity, color, or national origin; or (3) investigate extremism in the Armed Forces or DOD. The bill also requires the military departments to establish gender-neutral physical readiness standards. DOD must freeze the number of civilian employees who perform tasks related to diversity, equity, and inclusion (DEI). DOD may hire only one DEI employee for every 2,000 members who join the Armed Forces. The service academies may not employ as instructors individuals who are not members of the Armed Forces or civilian DOD employees unless no member or DOD employee may be adequately trained for such purpose. DOD must appoint a Director of COVID Policy to determine and implement actions regarding members of the Armed Forces who are involuntarily separated solely on the basis of refusing to receive a COVID-19 vaccination. DOD must submit a cost-benefit analysis and certain certifications to Congress in order to use federal funds for environmental projects.