How would you maintain ideology in the military? That's just the same problem but with guns and camo.

In the Middle East and Latin America, it is usually done by just not having civilian control of the military and making sure all the high-ranks and all the officer training schools are packed with ideological loyalists so you have a "deep state"/"state within a state" (originally meaning of the term was for right-wing military staffs during the Cold War). Of course, it is a very risky strategy and requires civilian control in the first place then relinquishing it.

Also, ye I've read parts of the Federalist Papers and it's kinda amusing what the different state of the things they proposed it now!