They want to present themselves as moral. What better endorsement than by being rejected by the US military under Trump? You get the people who hate trump and the people who hate the military in one swoop.
At the same time its kind of a non story. Anrhropic says it doesn't want its products used in certain ways, US military says fine, you can't be part of the project where we are going to make the AI do those things. Isn't that a win for both sides ? What's the problem?
It would be like someone part of a boycott movement being surprised the company they are boycotting doesn't want to hire them.