I've been both a uniformed soldier and a contractor, never an agency civilian but work with plenty of them, and they are not "in the military" in the sense you

I've been both a uniformed soldier and a contractor, never an agency civilian but work with plenty of them, and they are not "in the military" in the sense you mean here. They work for the military, as do I as a contractor, but we're not subject to UCMJ. If you're subject to UCMJ, then yes, your freedoms are severely curtailed and you do not enjoy the benefits of the Constitution afforded to civilians. You can be detained against your will by your commander. You are absolutely not allowed freedom of speech or freedom of movement. You can't quit the job. You can be fired for being fat. None of that applies to civilians, even DoD and IC agency civilians. If a civilian doesn't do what their manager asks, they can be fired. If a soldier doesn't do what their commander asks, they can be arrested. Huge difference between working for the military and being "in" the military.