The general public by and large is totally in the dark. It's been suggested that there are government types that keep incidents under wraps, but that they don't typically get involved with the supernatural world at large, at least not directly.
The supernatural community isn't quite so big on the conspiracy angle. They take some precautions to not draw attention to themselves, but they more so just bank on the general public's inability to accept the truth, and that they will just make things up to cope. "That wasn't a zombie I saw, it was just some homeless guy on drugs.", "That couldn't of been a bunch of werewolves, it must of been a pack of wild dogs or wolves that wandered into the city limits."
It's also worth noting that It's an unspoken rule of the supernatural world that you NEVER intentionally get the mortal authorities involved on any large scale. That It's considered to tantamount to launching a nuke at an opposing nation.
In short, the PC's (and GM) should be mindful of the vanilla population, but they shouldn't let it hobble them either.