Excellent way to put it.
There is room in the US Army for Jordanians, Egyptians, etc, PROVIDED there is strong evidence that they are NOT active Muslims. To the extent that somebody is a Muslim, then they are bound by their religion to be the enemy of all who choose not to submit to Islam.
Evidence that somebody is an active Muslim should be treated the same as evidence that somebody is an active member of the Communist Party, or a neo-Nazi organization.
You might not remember the Senator from Wisconsin that tried to shine the bright lights on the communists in our government. Joe sure raised a commotion for awhile. Then the communists got a law passes so that they would no longer have to swear alegence to our country. From that day everything has been going down hill. Lately, it seems that the speed of decent is accelerating.