The concept of being the gray man is more of an internet myth then real life thinking.

On your next commute to work, whether by car, transit or walking. Do you actually see someone purposely trying to be the gray man? In all likelihood, probably not. You are far more likely to see people dressed casually or dressed business casual or in full business attire making their way to work, shopping, out for a walk etc,

Even after big events such as 9/11, the northeast blackout of 2003 where 10's of thousands of people made their way home on foot, I don't recall seeing or reading where people changed their clothes and mode of thinking to gray man due to some further imagined threats to their well being.

Yes, a lot of people who were prepared, may of had a change of clothes or more comfortable shoes or boots but they were in the vast minority. Most simply and safely made their way home or to other alternate destinations with what clothes they had on without resorting to being the gray man.

That all said. If you wear a business suit into a rough and rundown area of town or conversely you wear a cutoff shirt, shorts and old dirty runners into the business district of any major city or area, you will stand out and will attract a lot more attention. Whereas someone who is dressed casually and who does not suffer from the mythical gray man mentality would easily blend into either area without notice.

Another similar subject. The other internet myth of being dressed in some type of a uniform with a hard hat or other prop such as carrying a clipboard in some crisis event is supposed to help you gain stature or access to something that the person standing next to you cannot...I don't buy it and never have heard of any reliable and verifiable source where this has occurred.
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Earth and sky, woods and fields, lakes and rivers, the mountain and the sea, are excellent schoolmasters, and teach some of us more than we can ever learn from books.

John Lubbock