Well, that's an interesting question, Not. According to my anthropologist professor friend, all cultures have gender (in the old-school social sciences sense of socially and culturally sanctioned roles/behaviours/dress codes/occupations deemed appropriate for one sex or the other). But two things are worth noting.
First, there's considerable variation from one culture to another (Medieval Iceland, modern day Navajo culture - weaving is a woman's job, Medieval England - weaving is a man's job). Some jobs do tend to be reasonably stable across cultures, largely for physiological reasons (big game hunting, ploughing with heavy draft animals - both men's jobs in most cultures because of the need for strength; looking after babies and toddlers - women's work, because of lactation).
Second (and relevant to this discussion) an individual culture can adopt either a flexible or a rigid attitude to gender roles. So a woman does a traditionally bloke thing - is the response of the people around her "bit eccentric, but each to their own..." or is it "stone the witch, she has transgressed the order of nature..."?
So called "third genders" (two spirit people in some Native American tribes, Sworn Virgins in Albania, Bacha Posh in Afghanistan, Hijira in India, etc. etc.) tend to be more common in cultures with very rigid gender roles. In other words, while there may be a physiological/neurological element to dysphoria, it is enhanced/damped down by whether it's easy or hard to be gender non-conforming in a given society. Almost as if "third genders" act as a sort of safety valve to blow off steam in a society which insists on rigidly pigeon-holing people.
I personally don't think it's an accident that the huge rise in trans identifying teens is coinciding with a backlash against feminism and a society which seems to have gone backwards over the last twenty years in terms of how hard children/teens are forced into gendered boxes (the pinkification/khakification of childhood, the Kardashian plastic barbie doll look for teen girls, toxically hyper-masculine role models for teen boys).