This isn’t over foreign policy but, rather, national security.
“Over foreign policy the governors have no legal say.” Governors DO have legal requirements to defend their citizens from all enemies, both foreign and domestic.
These ‘refugees’ aren’t even coming as families.
Make of it what you will but the law is clear - since this is a matter of Presidential digression (and as such a foreign policy plank), he and he alone decides, unless Congress rewrites the law and he signs it - unlikely. National security also falls under the President’s authority. The States long ago ceded their authority to override a Presidential decision - see US Civil War.