In early TNG (Season 1, Episode Angel One, I think it was established that only Starfleet personnel are bound by the Prime Directive).
Federation citizens however, might not be bound by the PD:
Captain's log, stardate 41636.9. As feared, our examination of the seven year overdue Federation freighter, Odin, disabled by an asteroid collision, revealed no survivors. However, three escape pods were missing, suggesting the possibility of survivors.
RAMSEY: Five months in a rescue pod no bigger than this room is an eternity I hope none of you will ever have to face. When we finally made it here, we thought we'd died and gone to heaven. You've seen the women of the planet. They're tall and strong and lovely. But after the newness wore off, we started to see how the men were treated. There's no votes. There's no opinions. There's no respect.
TASHA: None of which is your concern any longer, Mister Ramsey. Call the others in, please. It's time to leave.
RAMSEY: Despite their problems, Lieutenant, we happen to like it here on Angel One. We're not going anywhere.
TROI: But Mistress Beata
RAMSEY: Mistress Beata be damned! Her wish is not my command, and neither is yours. You can't force us to go.
DATA: Mister Ramsey is correct, Counsellor. The Odin was not a starship, which means her crew is not bound by the Prime Directive. If he and the others wish to stay here, there is absolutely nothing we can do about it.
RIKER: There's no time to debate the issues. You're going with us whether you choose to go or not.
DATA: Excuse me, Commander, but removing any of these people against their will would be a violation of several Starfleet regulations, not the least of which would be the Prime Directive.
RIKER: I realise that, Mister Data. I'd rather face a court martial than live with the guilt of leaving these people to their deaths. Commander Riker to Enterprise.
I'm puzzled though... a freighter is not a starship?
Huh... it basically has most characteristics of one with a modified design to haul whatever supplies it was designed to haul... but, ok.
It might not have been Stafleet strictly speaking, but the Odin WAS a Federation freighter.
So it seems that non-Starfleet individuals are not bound by the Prime Directive... but I would imagine that because majority of Federation individuals would be exposed to relevant general education, critical thinking and problem solving, I think they would implement a degree of self-restraint more or less (at least the majority might) when it comes to interference in other cultures.
Vash certain wasn't a Starfleet officer. She was Human, and as such a Federation citizen (quite likely - because she did later on appear as a member of an archaeological council in Season 4, Episode QPid)
She didn't care about breaking rules of a planet to go exploring and finding archaeological artifacts (most likely because the PD didn't apply to her).
So, it seems that PD applies mostly/only to Starfleet personnel... those who aren't in Starfleet don't seem to be bound by it (strictly speaking).