As for why some in the military support the GOP (I don't know that it's overwhelming though), it's obviously based partially on the tendency of Republicans to be strong(er) supporters of national defense and defense spending. And a lot of Republicans will play on patriotism, whether it's fake or real. While more than a few Democrats or liberals come off as not being very respectful of the military. That perception may be accurate or not. But at the same time, it's a mistake to think that all soldiers are like the Gunnery Sergeant from Full Metal Jacket - especially the millennials that are going into the military these days. Hell,
some vets are even supporting Bernie. People join the military for different reasons... always have. Some really are filled with a patriotic and service to country spirit, while some others just see it as an opportunity to improve their station in life; stumbled through high school, so joining the army beats working at McDonald's after graduation. Just like anything else, some people are devoted to what they're doing and some are just beating in their time.
My uncle is a Vietnam era vet and he is supporting Trump. He is a major (MAJOR!) law & order type guy. He started out on the Chris Christie bandwagon and then transitioned to Trump because he believes the tough talk that The Donald spouts out. I know another fellow who is a Vietnam era vet (former Perot supporter, like myself), and he hates Trump with a [NOBABE]purple passion[/NOBABE] because of what he said about John McCain, and how he said it. Anyone who criticizes a fallen or captured soldier is pond scum in his eyes... especially if that person never served in the military, or worse, was a daddy's boy draft dodger. He can't stand Hillary either and will probably vote for Johnson. A fellow that I work with is a Navy vet pushing 50, and he likes Bernie and Jill Stein. Based on everything else I know about him, he's probably an outlier though
(in so many ways
). He believes in the concept of free lunches, so Jill or Bernie would make sense in his mind.
Animus/Strict makes a good and interesting point about the political leanings of the enlisted personnel versus the officer corps. That says something about the class divide, I suppose. Years ago, I read something about a similar class/political divide in the British army during and after WWI. Course, back then, the officers were quite often from the aristocracy. But still...