It's a silly shibboleth, but I automatically ignore anyone who calls it the Department of War or Gulf of America. Hasn't steered me wrong yet. They're telling me they're the kind of people who only care about defending fascism.
It's a testament to the broken information ecosystem we're in that many people genuinely don't know this. Most will correct themselves when told. I agree with you that those who don't are not worth engaging.
Depends where you at
(Spoiler: it's still legally called the Gulf of America)