That's not accurate. DOD suppliers weren't banned from having "any commercial dealings" with Anthropic. They were banned from using Anthropic for their work with the DOD.
"Anthropic a Supply-Chain Risk to National Security. Effective immediately, no contractor, supplier, or partner that does business with the United States military may conduct any commercial activity with Anthropic."
Presumably, according to the defenders of the designation in this thread, this was an innocent mistake that doesn't indicate any political intent.