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What you must remember is that in the Federal military or any professional military for that matter the men are appointed and assigned by the political powers that be.
To refuse in even the sliest way is grounds for dismissal or transfer. To put it quite simply The Federal military will not rebel against the men who hold the power to dismiss, transfer, remove, or otherwise command them. They can’t, and as such they are incapable of upholding the Federal constitution when ordered to do otherwise.
They can only resign (thus joining the victims), or act covertly to subvert. (Presuming there is some form of resistance to aid with such information or efforts)
No one is required to obey an illegal order. Just because an order comes through the chain of command does not necessarily make it a legal order. Of course, with the general staff we have now there’s virtually no chance of any pushback against the CinC. They see their duty as protecting their pensions, not the Constitution.