I've wondered in the past if Starfleet would shoot down human missionaries attempting to bring God to some poor unsuspecting pre-warp planet.
It's difficult to see why Starfleet would. If the prime directive indeed doesn't apply to non-Starfleet individuals, then there would not be any restrictions on sending out missions to various worlds, pre-warp as well as post-warp.
How often would civilians be on the frontier, away from the Federation's core worlds, or just away from warp-capable civilization in general?
The primitive (let's just use that word) planets are probably all around, wrapped around, the more advanced planets. Out of every 100 planets with intelligent lifeforms, maybe 99 are primitive.
So, it wouldn't be a matter of traveling away from the core systems. The primitive planets are intermixed with them.
Else the missionaries would have to explain how they're not gods, even though they appeared miraculously from thin air and even though they command other god-like powers ...
Native: You appeared out of mid air, are you gods?
Missionary: No, that's just how we travel long distances.
Native: Sister Kimiko cut her arm badly last badly and didn't die, is this magic?
Missionary: No, she washed it with soap. You get some animal fat from yesterday meal, I'll get some ashes, and I show you how to make soap. Later I'll show you how to make candles.
