It is simple: "civilian" means "one under civil law" - as distinguished from one under military law.
Our military personnel are non-civilian. Everyone else is civilian, including police officers, firefighters, first responders, and teachers (all of whom I have seen erroneously referred to as "non-civilian").
There is very real danger in ascribing an "other than civilian" designation to those who wield the power of the state, because it implies that such people are somehow above (or outside of) the civilian law. Law enforcement officers enforce civil law. They derive their power, authority, and duties from civil law. In carrying out those duties and exercising that power and authority, they remain subject to civil law.
This hits it squarely on the head! Atta boy Chip!
If you are NOT in the military and you don't have to do what Uncle Sam says, you are a civilian