John Clark, contrasted against James Bond. This has some very obvious benefits for anyone in rough situations.
The grey man is an intersection of skills and oblivion. No matter what he knows or carries, he strives to be completely uninteresting, just like his namesake. He can neither give nor take offense at others while remaining grey. He cannot be flashy or overly ebullient. The goal is to simply be "some guy."
There are many places where you may be standing out right now that can be made more grey.
This is one of the biggest areas of distinction. Clothing is visible to everyone who sees you. As you attempt to become more grey, consider how your clothing fits into your surroundings. The neon shirts I wear every day to work blend in perfectly on a jobsite, but stick out like a sore thumb in the grocery store. In the blue-collar area where I live, my t-shirt and jeans are almost the neighborhood uniform. Visiting my wife's office, they make me very noticeable.
As a general rule, avoid flashy jewelry and doodads. I also try to avoid shirts with printed messages or designs, unless they help me fit into an environment. At my local nerd store, I can be grey wearing any manner of geeky shirt, because everybody else wears them. At a sporting event, a shirt from the home team is ready-made mental camouflage. The running joke among my friends and family is that my "Dude uniform" is a one-color t-shirt and a pair of jeans. It's simple and effective, and goes completely unnoticed.
Another major identifying item is what you drive. That big bad bug-out wagon that can ford rivers and carry 3 months worth of supplies is effective, but everybody sees it coming. I love a flashy car as much as the next gearhead, but flashy stands out. At my place, our daily drivers happen to be white, domestic, very popular models. My wife's truck has no bumper stickers or other showy bits. My truck has one sticker on it from before I bought it, that I just haven't gone to the work to remove yet. Both of them are well-maintained, but outwardly appear entirely bland. If I want to make an impression, I have a flashy little sports car, but outside of that, the sports car stays in the garage in favor of the boringly effective truck.
The way you move, act, and speak can very quickly make you noticeable or invisible. Acting nervous, excitable, or overly agitated will immediately mark you in the minds of people around you. Don't be overly specific about skills or other preps unless the situation specifically calls for it. Being pleasantly aloof and noncommittal will make people forget you as soon as you walk away. Be polite and pleasant and you'll fade into the fog of the hundreds of interactions humans have daily.
Tattoos, piercings, and other body mods also stick out. If you're trying to disappear, identifiers like those are going to have to hide. They're colorful, unique, and permanent. All of this is fine, but it makes you stand out in peoples' minds. If you have body art, consider how to camouflage it if the need arises.
The moral of the grey man is "Don't advertise." Businesses advertise to get attention. Grey folks do the exact opposite to achieve the opposite result.