Members of the US military swear to support and defend the Constitution of the United States against all enemies, including domestic ones. Just because your family members might be oathbreakers doesn't mean everyone in the military is.
Whoa, that's harsh. Actually, military abandoned one of ours leaving them to die despite excellent, decorated performance. Had to get home on his own who knows how through the Middle East. Others came and went the ordinary ways. Different soldiers in the family have different perspectives on the military. None are affecting what I'm saying except as anecdotal support about how loyal soldiers are to military during their terms & maintaining close relationships afterward in many cases.
Far as Constitution, soldiers all do swear it as they're told to. Some mean it, some don't. Yet, the liars that got more soldiers killed in Iraq than 9/11 are still alive and free despite all those soldiers' oaths about domestic enemies. Many soldiers continue to serve under these corrupt politicians and even hit new targets on basis of their word. More importantly here, the military and civilians working in the mass collection programs are all working hard at eliminating Constitutional freedoms in terms of 4th and 5th Amendment while watching their leaders lie under oath about it. Can count who came forward on one hand out of thousands to who knows how many. That's saying something.
The disconnect between that and you're statement is that you're ignoring that each member of the military has their own view of what doing their duty is which is usually highly biased. Most of them at least start with the one instilled in them by American culture (pro-military mostly) and military indoctrination. Guess what the military indoctrination didn't teach them? That secretive organizations in the military and intelligence sector are spying on all Americans' data feeding stuff to law enforcement and other groups that has nothing to do with terrorism despite what the law said about that. That they need to oppose or take out those organizations. Instead, they're told to believe and do what they're told by such groups even if it supports illegal SIGINT efforts. Most do at least for the duration of their service. Many will think of fellow soldiers as an extended family of sorts afterward.
So, believing the loyalty of military personnel is to the military is a suitable default. Unless we get hundreds of new leakers soon and all kinds of soldiers storming Washington for sole purpose of getting rid of corrupt politicians that have them killed for selfish gain. I don't see either. Most of them must be on military and politicians' sides in practice. Or just apathetic, which is its own danger.