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Dear Ms. Riley,
Thank you for posting your request on History Hub!
If any military demographic data about religious preferences/affiliation has been collected over the years, it may have been part of a survey or database. The Defense Technical Information Center (DTIC) may have data and it may be part of one of their public databases. Please check their web site at https://discover.dtic.mil/ for this possibility. Or it may have been accessioned by NARA and is in the custody of the National Archives at College Park - Electronic Records (RDE). Please contact RDE via emal at firstname.lastname@example.org to check if they have the information you seek.
If the military has not collected this data as part of a database, you may have to compile it by visiting the National Archives at St. Louis (RL-SL), the National Archives at Washington, DC (RDT1), and the National Archives at College Park - Textual Reference (RDT2). Please refer to NARA’s web pages on planning your research visit.
We hope this information is helpful. Best of luck with your research!