I'd set aside a few minutes before the next session to discuss this, completely out of character and outside the actual game. Let them know you want to have a Meta discussion about NPCs and the world in general.
Lay out the fact that, as GM, your job isn't to murder/slay/kill the party, but to be the filter between the player and the world. That your NPCs are not and cannot always be evil villains or servants of the dark masters, so they need to understand that their reactions are not appropriate to the setting.
But first, I'd ask Why they are so on edge. For example, I had a GM that, over several unrelated RPG mini-campaigns, set villainous NPCs in our path. After that, we never trusted his NPCs again. We just assumed the NPCs were sleeper agent assassins biding their time, because of those assassin NPCs that had attacked a few parties in the past. We were paranoid and on edge because of him as GM, not because of the RPG setting/session/story. That was a meta-game decision. But we just sort of assumed that's how it would go down, because it had gone down that way a few times already. To the point that we refused the help of NPCs when we shouldn't have. It is possible that one or more players have had similar experiences with past GMs and simply assume that's how RPGs work. It would only take one player to sew the seeds of paranoia and doubt in the others.
I'm not saying that's what is happening here, but something like that might be happening here.
I also think Dale M's suggestion of color-coding areas is a good idea, though I would make that a temporary thing. Use it as a tool to help them understand that some areas are safer than others, but if it works, after a few sessions, start phasing it out. Maybe forget to set the tiles out and wait for them to ask. Or just say, "Your characters aren't quite sure how safe this area is..." But then make sure to follow that with "That's not a threat, no really!" But they shouldn't always have such clear-cut safe vs. not-safe zones. Eventually. When they are ready.
One last idea, that you sort of hint at. Maybe that's the game the players want to play. If they truly prefer a high-paranoia style of game where they can't trust anyone "outside" their team, then perhaps you should try to shift the game, at least somewhat, to support that. If so, that should come out when you ask why they're on edge. But set up some boundaries. Maybe require that each PC have a set number of NPCs they trust implicitly (or 1d6 NPCs, or whatever). Help them work up who those people are -- not stats, just how they know the NPC and why they trust them. Use at least one of those NPCs in each session as a link between the PCs and the world that isn't threatening. As an aside, a horror writer once told a convention panel that horror isn't the threat of death; it is the threat of watching your friends or loved ones die and being helpless to prevent it. If they want a horror game, then NPCs they trust are an implicit way to make it horrific.
But that's going darker than you want, so I'm leaving that as more of a general thing for other readers. I don't think it's the direction you want here.