You say that like physiology (including brain chemistry) has no influence on behaviour or development. Male monkeys prefer trucks and female monkeys dolls, without any societal pressure to conform with traditional stereotypes. Human girls exposed to higher levels of testosterone or androgen during prenatal development will often exhibit more 'masculine' toy preference and play behaviour, even if their parents encourage 'feminine' toys and behaviour.
There's also the matter of transsexuals, few if any of whom would go through an aggravating, difficult and often dangerous transition if there was an easier and more straightforward approach, though sadly there isn't. There is a bit of a problem where some people won't accept that it's a necessity and still insist it's playing on gender stereotypes, though I think that position is becoming increasingly marginal, thankfully.
