I think you're missing the concept.
Grey Men don't go into those kinds of situations with the intention of remaining grey.
The concept is that you're already in a bad sitch. You get caught at work, say, when TEOTWAWKI happens. The usual scenario is that you're traversing some area in order to get to a known location, like your home or your bugout location or your car or something. In that situation, the Grey Man tries to blend in until he can get to that location. You're not leaving someplace and jocking up to plunge into the maw of the Antifa city; you're just trying to get from Point A to Point B with as little grief as possible. Grey Man is a state of mind and a type of behavior, not a specific tactic.
TL;DR: if you're in a situation where you need to carry "things you might need," then it's not the right time to be the Grey Man.