Man-related refers to genders that are related to, but not aligned with, being a man. Man-related people are not man-aligned at all, but feel as though they're in the same "category". Similar to how blue and green are different colors, but they’re both still considered “cool colors” and are in the same category, or how hyenas and cats are extremely different animals, but are both a part of the same suborder. It is something completely separate, but connected in some way.
The feminine equivalent to this is woman-related.
Flag
The man-related flag was made by Tumblr user quiet-times on November 1, 2020[1]. The stripes have no written meaning, but are presumably to represent colors that are similar, but different, to traditionally masculine colors, like blue.