I'm not Spartacus, and I am late to this, but I wanted to reply to this comment.
But if we believe (as I do) that gender is a social construct, isn't it equally problematic to say that a boy who likes pink and sparkes is going to grow up to be a gay man, and a girl who likes drills and pirates is going to grow up to be a butch lesbian? Surely sexuality is as divorced from the nonsense of "gender" as biology is?
I have two related points here. One is, there's a methodological issue here.
The majority of children do not go on to become homosexual adults. Therefore, even if 100% of homosexual men had adored pink sparkles aged 3, you could still very easily find that liking pink sparkles was a rubbish predictor of male homosexuality, couldn't you? Because there could be a much larger group of heterosexual males, who'd also loved pink sparkles aged 3, and who would mess up your data.
That's probably a side point - but it shows how important it is not just to look forwards from the child ('how will he or she grow up') but also backwards from the adult ('what was he or she like as a child, and what did we - or society - insist that meant?').
I mention this side of things, because I think this is where the issue with gender dysphoria and sexuality becomes interesting. And this is my second point.
I don't believe there's anything innate that would make little girls who're going to grow up to be lesbians, gravitate towards boyish toys/activities. But there is a powerful socialised reason. If you are a small girl who listens to stories about the prince who gets the princess, or who sees that the man who plays football marries the lady who wears pretty dresses, you take messages from that. And if you are a small girl who relates to the prince getting the princess or the man marrying the lady, you may end up thinking that in order to be the person who gets the woman, you have to be masculine. Right?
I base this on my DP and a lot of her friends, btw, though I was also a tomboy child who has grown up to be a feminine lesbian. It is also something that is often theorised by academics looking at the ways lesbians read fiction, which is something I'm interested in.
I think it's obvious that a lot of small children who engage in opposite-gender play are just playing. But I also think some of them might be gravitating towards those roles because society is heteronormative and has sent a message to those children that, to get XX they must be XY.