I don't know, I am just guessing because not a single American company has publicly stated they are against its product use up to a certain degree by DoD? If they have not publicly declared it then yes, DoD simply don't sign the contract.
So your argument is that the government is punishing Anthropic for its public statements? And it is correct to do so?
(I think it's also the case that Anthropic didn't make any public statements about the negotiations until after the DoD was already publicly threatening this designation. But that seems less important than the question of: is it good for the US government to try to destroy companies whose public statements it dislikes?)
Honestly I would find a certain satisfaction in a world where the next Democratic administration takes away Fox broadcast licenses, forbids use of Oracle by any government contractor unless Ellison hands CBS over to Rachel Maddow, and tells Bezos that Amazon is going to be banned from public roads unless the Washington Post front page has positive stories every day. But I doubt the same is true for the many pro-Trump people who complained vociferously about Biden officials expressing preferences to social media companies because of the merely implicit threat that they might take government action of some kind if they weren't listened to.