Oh, you mean invisible entities like mathematics, scientific laws, human languages, or "the laws of Nature and of Nature's God," as Thomas Jefferson put it in the Declaration of Independence? [Not to mention souls, which you deny "in principle" — a sector of reality to be adamantly denied — because it does not fit your presuppositions!]
I guess I'll have to check with xzins on this; for as a former military chaplain, he'd be the "expert" on this question, not I: I strongly doubt spiritual counseling is a mandated matter. But I am pretty sure it would be made available even to atheists, should they request it.
2) We're back to where we started because I never left. The world is what it is. You live and then you die. Make the most of life, is my advice. It's not rocket science.
3) My language doesn't reshape reality. Reality is what it is, simple, clear, and right in front of you. If you want to make up extra narratives with a metaphysical Good vs Evil endgame psychodrama, go ahead. But you're making it up. You're taking previous generations' fantasies and reinterpreting them for your own amusement. You're free to do this. Just don't try to make others do it.
4) As long as it isn't mandated and isn't too expensive, I don't care.
I believe spiritual evaluation, where appropriate, is part of a mandated psychological evaluation. If I understand the dispute properly.
I believe the Atheists want the "spiritual" evaluation deleted from everyone's evaluation. Apparently, the US military is to deny that anyone has spiritual needs.