The United States Military has always allowed aliens to serve. Check out the roster of Custer's 7th Cavalry. In fact the old I&N law stated that failure of an alien to report for induction was a permanent bar to citizenship, I'm sure that's gone now.
My Basic Training platoon at Ft. Polk in the summer of '69 had two aliens, both Latinos from Central America. One as I recall was not a legal permanent resident.
When I worked for the old INS in New York City in the early - mid '70s, my most aggravating "nothing" case involved a Haitian applicant for citizenship. The fellow was a student at Colombia but had served four years previously in the U.S. Army including a tour in Vietnam which resulted in his receiving a Purple Heart and a bronze star. While on a tour in Germany he married a German woman, that didn't work out and he came home one day to find her gone. Well the old boy comes in for his naturalization interview and the examiner asked about his living arrangements. The said decorated veteran repliess he shared an apartment on the west side with two other students, a man and his girlfriend. The examiner then asks if he's "done the nasty" with the female roommate and he replies in the affirmative. The examiner referred the case for investigation since the Vietnam vet was an adulterer. I "drew the black bean" and got this dog of a case I told my boss that this was the stupidest thing I'd ever heard in my life, he agreed but it had been referred so had to be done. I went to see the old boy, who deserved citizenship more than a lot of people born with it, and asked him about the details. He said he hadn't divorced his wife because he couldn't find her and other things, like finishing at Colombia were higher on his list. He said "I didn't know that to be a citizen I had to live like a monk." You could make an investigative comment on the report and for one of the few times I did stating that the case should never have been referred and was a waste of government time and money as well as an unnecessary inconvenience to the applicant.