One could take his assertion as it stands: That the military is disproportionately supportive of GOP administrations and tolerant of Dem admins. That is true. There are several reasons for that:
1) Under Obama, the size of the military was cut dramatically (smaller than it had ever been since 1940) in personnel, equipment, and funding. At the same time, the mission was not reduced.
2) Cuts in personnel were enacted partially by attrition (simply not allowing some troops to continue their service), partially by involuntary separation, i.e. firing (richly deserved in some cases), but also by just plain layoffs. You tell a mid-career Soldier thanks for your service, but there's no room for you anymore after 10+ yrs, multiple deployments, and no serious negative incidents? They'll tell you to go **** yourself to your face, unless you're the CinC. In that case, they'll wait til you leave the room.
3) Pay and benefits: No, the US military is not a mercenary corporation, but neither are we slaves. When we signed up, there was a contract entered into between ourselves and the US gov't. Federal law mandates certain benefits, such as allowance for housing. The Obama admin CUT (as in the benefit shrank) that benefit for most troops. Raises that are REQUIRED BY LAW to be a certain percentage were SMALLER.
4) Weenies like Chuck Hagel, Ashton Carter, Leon Panetta as SECDEF (interesting side note: during the process of sequestration, Panetta would use military transport to FLY HOME TO CALIFORNIA every weekend at a cost to taxpayers of $32k/round trip. Meanwhile, vehicles are sitting in motorpools rusting and cannibalized for parts)
Those are things we see under a Dem admin. Under a GOP admin, we get
1) More personnel, equipment, and funding: Reagan and Bush43 both increased the size of the military, and not even two weeks into the Trump admin, we are getting ready to grow again.
2)No cuts in personnel except for those well-deserved firings (seriously, you want to get a DUI? Beat your spouse? Abuse your troops? Enjoy being a civilian)
3) Pay raises greater than required by law, every year
4) Two Words: James Mattis