This must go by unit. I went to war and, although the environment was quite religion-friendly, it was not in any way coercive. I even thanked the chaplain for obtaining a bunch of paperback books for us to read during downtime. The books were generic, not religious, and didn’t come with any catch like attending a service or such. The chaplain deeply cared about the morale of all troops, not just the religious ones.
However, this isn’t the first story I’ve heard about a coercive unit that alienates the non-religious, through news sources and within the Army.
My daughter spent 11 months in Afghanistan and my son-in-law much the same amount in Iraq. I’ll try and ask them about this when they get a chance (they are in transit to a new posting at the moment and really would not be helped by me asking something like this right now).
That said, I’m still not sure that this wasn’t push-reporting and that the non- and anti-religious are notorious for construing every encouragement to religious expression to be toxic coercion.
I happen to know a number of chaplains and what you report is what they do and how the minister. They are there for whoever under whatever circumstance and do not ask about affiliation nor do they press for any kind of particular expression of belief. What the men and women on the front lines need is confidence and reassurance. That need not involve praying (though, as a priest, I naturally tend to that kind of expression) and the chaplains I know would not insist on it lest someone who needs care decides not to seek it. That could lead to diminished morale and might lead to injury and death from despondency and lack of resolve.