"I suppose this guy didn't know when he became a Protestant chaplain that he would be expected to minister to Protestants of all denominations?"
Actually, it goes way beyond that. He might well be expected to minister to Catholics, Jews, and even Muslims as a military chaplain. Comes with the territory.
Yep. He should find another line of work.
I think you will find that Catholics or Methodists would have no objection to praying in Jesus Christ's name. I doubt that a Christian chaplain would be asked to officiate at a Jewish service and frankly who cares what the muslims might think.