A 100% proper controlled experiment with double blinding etc. is not possible, perhaps, but there are transgender children who often are raised as if they were of their physical sex, which obviously causes them to suffer.

I always wondered - if it's purely a social construct that boys play with trucks and girls play with dolls etc., then why in most stories about a girl trapped in a boy's body we hear her say "I wanted to play with girls" (contrary to society's expectations), "I wanted to play with dolls" etc.?

I googled it up just now - http://prospect.org/article/transgender-candidate

The story of Bindaya Rana (from Pakistani), who was born as a male:

"Bindiya Rana, one of Pakistan’s first transgender candidates [...] “I used to wear my sister’s clothes,” she said. “And use lipstick and powder and nail polish. I wanted to play with dolls and be in the kitchen.” Her parents disapproved when they found her in makeup, beating her."

It's a gaping hole in the theory that we are wired differently "as we grow up due to the different experiences and upbringing men and women are subject to".

If one's self-identified gender could be overriden so easily, there would me much less personal tragedies in this world.