"Consider that, as a chaplain, he answers to a higher authority than just the officers in command over him? Chaplains are somewhat unique in the military, IMO."
Chaplains are still held to the same standard regarding chain of command as any other member of the Armed Forces. Your argument doesn't wash. He screwed the pooch on this and he knows it.
Yes, he's held to the same standard, but the issue here is a direct facet of his religion, and therefore also directly impacts his duty before God to adhere to his religious beliefs. The superior issued an arguably illegal order - considering that the chaplain's oath as an officer must coexist with his ordainment as a minister.
He will be punished. Heaven knows the military does not tolerate dissenters well - even when the dissent is warranted. In my opinion, it was warranted in this case.