I remember the story of Obadiah in 1 Kings 18 who, while in the service of King Ahab, clandestinely hid the prophets of God and cared for them out of Ahab's table. While Elijah appeared to have some disdain for Obadiah, God told Elijah that it was he (God) that had set aside the prophets. Obadiah was doing precisely what God wanted him to do in hiding the prophets.
Military chaplains to me are the Obadiahs of the world. They have to live with a government that is becoming more increasingly hostile to them, all the while serving God-overtly and covertly. It sometimes more easier to be an Elijah and fall on your Christian sword than to try to accomplish goals in other ways. It is a very difficult balancing act.
Matthew 10:16 “Behold, I send you out as sheep in the midst of wolves; so be shrewd as serpents and innocent as doves.
The difference now is that military service is entirely discretionary. I would contend that no real Christian has any business serving in the military to defend a country whose government is openly hostile to Christianity.