I know what you're saying, but it needs to be stated that police are also civilians.
It specifically mentions armed services, police, and firefighters are not civilians.
Civilian in law enforcement jargon means a non-sworn position: https://www.discoverpolicing.org/explore-the-field/civilian-...
To make this more interesting, Posse Comitatus employs the language to signal "non-Federal forces" eg: National Guard activated by a state to operate domestically are referred to as "civilian law enforcement".
In any of the above cases, calling LEOs civilians would be incorrect and would eschew them of many of their responsibilities.