When my sons registered with Selective Service, along with the usual little card, they filed specified "conscientious objection" documents with Selective Service, our elected representatives at every level (even our county sheriff's office), and with the Department of Defense, based on their Biblicist Christian upbringing, faith, and practice.
1. Cannot serve in close quarters or combat with women.
2. Cannot serve in close quarters or in combat with admitted sodomites (homosexuals for the politically correct minded).
3. Cannot serve under United Nations command, or as anything but a clearly identified United States soldier.
4. Cannot serve in any capacity where open, verbal witness for Jesus Christ is forbidden.
5. Cannot serve in any capacity where the consumption of alcohol is a prominent feature of military socialization.
. . . and several more items.
I couldn’t imagine the military even considering accommodating those conditions, but don’t worry: This country will never have a draft again. Nobody would show up.