<<Do you have a problem with listing the religious preference of a soldier on their dog tags?>>
Depends on the soldier's consent. Here's a true story for you from my late friend and neighbour, an English soldier who enlisted in 1939, was wounded in France, evacuated at Dunkirk, fought again in the Middle East and Greece, was captured, escaped and recaptured. Before his unit shipped out, the officers called the whole group together and offered the Jewish guys a choice of fake dog-tags showing them as members of several main-stream Protestant churches, which had agreed to the deception. (The RCC had been asked and refused to participate.) Every one of the Jewish soldiers refused, and nobody pressed them on it. This issue was left until the eve of the embarkation. At that point, the officers went round to the Jewish soldiers in private and repeated the offer, but this time the men were told, this is your last chance - - we ship out tonight. There won't be any more chances. If the Jerries get you and find out you're a Jew, we can't vouchsafe your treatment or your safety. At that point, every Jewish soldier in the unit took the fake dogtags.
My friend told the story as an example of the British Army's superb understanding of soldier psychology. They knew that the boys' egos needed the opportunity of rejecting the first offer, demonstrating their bravado and acting like big shots in front of their buddies, and they gave them that chance. They also knew that a soldier would have to be nuts not to take advantage of the offer and that those who through stubbornness or pride had refused it in front of their mates, would agonize later, when it was too late, about what could happen to them if captured. Hence the second offer, on the eve of the embarkation. In short, they knew that the first offer would be turned down and that the second would be accepted.