My wife works in Early Childhood Education, and we have a young daughter, so this sort of stuff comes up a lot.

There's no single consensus on this sort of stuff. There rarely is on the social science things, since anything involving dealing with human nature has too many variables to account for them properly on a broad scale.

But what we've observed over the years (combined with actual empirical evidence and knowledge my wife's education and career) is that it's not so much the biological things that tend to mess up young kids (hormones, genitals, etc).
It's that socially we genderize so many things that have nothing to do with what biological traits you have.
Like colours. Or vehicles. Or even attitudes and expectations.

So it's a bit of a "grass is greener" scenario.
After all, they're still new to the world, and have been told from birth "you are a boy/girl. That means you will look and act a certain way."
So then at some point the kid thinks "boys/girls get to do (insert genderize activity). I want to do that, so I must also be one."

But that's just because the gender is defined to them as whatever stereotypes people around them fall into or impose, so they'll assume that if they don't perfectly match what they've been told their gender is and how it acts, then it must be wrong.

A boy in a less oppressive household might be free to try make up without feeling that it defines anything about whether they're a boy or girl.
Whereas one in a more stereotype-imposing household might want to try make-up and therefore assume that must mean they're actually a girl.

So weirdly, I think the people who impose the gender stereotypes more harshly are more likely to have a young kid who thinks that way, since they aren't free to just express themselves how they want. Especially when they're young enough to be getting an identity but lacking world experience.