Because Anthropic sells Claude through other companies that in turn do business both with Anthropic and the government. These intermediaries, large cloud companies, can't offer Claude anymore if they want to keep the government as a customer.
The government is faaaaaaaaaaaar too invested in Azure and AWS for Microsoft or Amazon to give even half a shit. The DOD has no where else to go and the companies know it. They'll sit on their hands until the legal maneuvers play out, which will take longer than this administration will be in office.
But thay doesn't imply they can't do business with say the German Federal Government for example?