Are people seriously thinking of letting LLMs control weapons?
No.
But giving someone who isn't the government the power to tell the military what it can and can't do seems like something they should object to categorically rather than case-by-case.
Trumpists ... thinking?
If you classify Pete Hegseth as a person, then yes, apparently. Or perhaps he's only into the domestic surveillance angle---IIRC those are the two things Anthropic doesn't want anything to do with.