I will call BS on people who say that they still abide by their oaths. Perhaps they should say "part of it." Now it's a given that you don't have to follow the orders of officers, since after leaving the service, there are no officers you are bound to follow. But what about the president? As a soldier, you had to follow his orders regardless of whether you agreed with them or not. Now, I suspect, depending on party, you'll find many that would be more apt to tell a president to pound sand than follow his or her orders.
True story. A pal of mine actually left the service when trump was elected. He said he refused to take orders from him so when he got a chance he got out.