xzins is a chaplain. Pinged him to the discussion.
My fear is that the military will deal with any conflict by simply ending the chaplaincy. There is no requirement to have it. That said, it will be clearly unconstitutional to force a minister to function in a government approved manner in the conduct of religious ministry. Most denominations view marriage as religious., so there will be no required weddings. However, I can envision required counseling which is not necessarily viewed as religions in nature.