The Department of Defense (DOD) Instruction 1300.17, "Religious Liberties in the Military Services," conveys support for religious beliefs in the following statement:
"In accordance with Section 533(a)(1) of Public Law 112-239, as amended, the DOD components will accommodate individual expressions of sincerely held beliefs (conscience, moral principles or religious beliefs) which do not have an adverse impact on military readiness, unit cohesion, good order and discipline, or health and safety. A service member's expression of such beliefs may not, in so far as practicable, be used as the basis of any adverse personnel action, discrimination, or denial of promotion, schooling, training, or assignment."
All of the components in the military have a similar process for various religious accommodations, including vaccine exemptions. The Army's religious accommodation request process, which takes 30 – 60 days, is outlined step-by-step in Army Regulation 600-20 (AR600-20) Appendix P-2: