"What I do find to be incredible is that they have told chaplains not to proselytize on duty."
Why would you find that to be incredible? I'm not sure it's the government's responsibility to proselytize a particular religious belief system. Matter of fact, it's probably a Constitutional violation.
Chaplains are there for counselling and support at the behest of servicemembers. Nothing more.
Better read your Constitution pal. It contains NO prohibition against prosylitizing. Nor does it contain words requiring separation of church and state. It DOES contain words prohibiting government interferance in the practice of religion.
Well, that is your take on their duties.
I have had many chaplains invite me to come to their services, and believe me, that creates no pressure whatsoever. That is proselytizing, as is explaining what their religion is, later on after the service.
They wouldn't be good Christian ministers if they didn't.