Roman Catholic is not the only "Christian" Catholic in the US, there are some Opus Dei/Rad Trad types who believe that since Vatican II, Rome was no longer Catholic enough for them, and they only nominally listen the Pope.
Especially a lot of the pro - Fascist US Bishops who are butt-hurt over being called out for property/financial shady dealings and of course, the child abuse they had been indulging in since the mid-19th century. There's enough political tension around the US bishops and Pope Leo that some former (disgraced) bishops have been talking about a split, as there is with the various Eastern Orthodox churches.
So, as was explained to me by various Catholic devout over the years, using the term Christian Catholic does not necessarily mean Catholic following the Pope in Rome.
It could also mean member of a Latin Mass strip mall "Catholic" church run by a former deacon or Dominican seminary student who went Rad Trad.

but exactly are the consequences of not being listed as Cristian?

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.

while his mouth is steadily working overtime.

Link to tweet

that "Mormons aren't real Christians." I'd argue that most fundamentalist Christians aren't Christians, either, based on the words supposedly said by Jesus Christ himself, but what do I know?

Bottom line is that Hegseth is one of those fundamentalist, dominionistic Christians. They think they are the only arbiter of what is Christian and what is not.

This is all silliness. The military should have nothing to say about the categorization of religions. In fact it is prohibited from doing so by the Constitution. So is Hegseth.

And this articule saying “sect” is doing some major editorializing

The defense secretary has spent most of his tenure drifting from one culture war priority to another. Evidently, he hasn’t gotten to the end of his list.

On the one hand, Hegseth is using his office to advance a Christian nationalist agenda.

On the other hand, his Pentagon isn’t just elevating one faith tradition, it’s also demoting other faith traditions, slashing the number of religions the Defense Department officially recognizes.

— Steve Benen (@stevebenen.com) 2026-06-05T21:02:17.897Z