I would like to point out that the military hires Chaplains to maintain the morale of personnel. Thousands of Chaplains have done so and do so today without becoming sectarian. Only a small minority cannot contain themselves, preach their sectarian beliefs to mixed audiences, and play the victim card when called out on it.
This is not limited to just using the word “Jesus” in invocations. Other expressions of both favoritism and dismissal occur, and these are deeply offensive to people of other faiths. Some of these Chaplains also confuse their sectarian beliefs with military policy. Again, they are a small minority.
But this is not the purpose for which they have been commissioned.
Some years ago, there was a major scandal at the US Air Force Academy. Favoritism was shown to cadets by cadre on the basis of religion. When exposed, the argument was turned around so that supposedly being told to discontinue this favoritism amounted to persecution. This is nonsense.
The majority of Chaplains perform very difficult ministries, yet have no conflict with obeying the rules and regulations. In turn, this reduces sympathy to those who cannot.
I would like to point out that chaplains are divided into groups to avoid conflicts with other religons: Protestant, Catholic, Jewish, Muslim. So anyone who is insulted by one of these need not return to that religous service but seek out a service where they wont feel insulted.