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.
Basically, if you don’t like a religious environment, then don’t join the military. The military is fine for reasonable atheists, I was an example, but militant atheists or anti-Christians just won’t be comfortable with all that religious expression going around. BTW, our chaplain educated himself about Judaism as much as he could so he could at least help out the Jewish soldiers in my unit. Rabbi chaplains are apparently kind of rare. We also had a rather outgoing pagan soldier, everybody liked him.
As with all large organizations you will eventually get bad apples, in this case commanders or chaplains who consider it their mission to make it hard for non-Christians. They’re a throwback to hundreds of years ago when it was considered acceptable for Christians to convert by the sword. This is not allowed in the Army, and the Army has mechanisms to deal with it, from going higher in the command, to the IG, to a congressional.
BTW, tell the kids thanks from me, and to keep their heads down.