Only U.S. Citizens should be allowed to serve in our military. Period!
I basically agree with you here too, if you serve you should swear exclusive loyalty to the U.S. and the Constitution (I did not personally serve, so I am not 100% sure if this isnt the case already).
But if someone is willing to put their life on the line for our country they should be given some sort of fast track to become a citizen, assuming they have been honorably discharged.