When a chaplain is leading a service for those of his own faith, he should be able to pray in accordance with that faith. However, when a chaplain is saying a public prayer, for a mixed-faith group, things are different. The chaplain should respect the faiths of all those in his audience.
I'm not a chaplain, but I've been frequently asked to lead the invocation at our gun club's annual banquet (for all I know, maybe I'm the only one there who knows how to pray, or is willing to pray in public). Anyway, because the Club membership includes Catholics, Protestants and Jews, I always make my prayer non-denominational.
When I attended Squadron Officer School back in 1957, we had a lecture from the school chaplain. The lecture was about the chaplain's duties. This particular chaplain was a Protestant, but he pointed out that part of his duties were to see that a Mass was said for Catholics, which meant that the had to find a priest if no Catholic chaplain was available. The point is, a chaplain has two kinds of duties. One is to provide for the needs of those troops of his own faith. The other is to see that the needs of troops of other faiths are met, even though he cannot meet them himself. Therefore when he leads a public prayer as part of an official ceremony, his obligation is to respect the faiths of all those present. This can be satisfied only by a nondenominational prayer.
Granted, it might be difficult to find a nondenominational prayer that satisfies Wiccans or Satanists as well as the three most common religions in America, but I've never had to deal with that problem.
Well said Joe. I'm a chaplain and what you just described is exactly what we are taught from day one.