And the enlisted Religious Non-Comms who act in lieu of the Chaplin are determined/assigned by the recognized religions on the list.
As White Nationalism takes over, fewer and fewer religions will be recognized.
The first non "Christian" Chaplains were Jewish and Roman Catholic, appointed during the Civil War in 1862.
But I can guarantee there were probably Jewish, Catholic, Muslim, and other sects of religionists and non-religionists in the US military since the beginning to that time who weren't being served by the Chaplin Corps (who were also supposed to help the illiterate with news to and from home along with other personal issues affecting their ability to do their duties) because they didn't show up at services.
On edit.
If the US military "leadership" can limit the Chaplain's Corps to only reflect the "Official Religion", they turn the Chaplain's Corps into Political Officers instead of the Mental Health and Personal Ombudsman service they currently supposed to provide, which is a throwing away of trust between the Military Personnel and the State they serve.