> with whatever they want

That's the key point. I've observed that ones tend to want one things and the others tend to want other things.

Of course there's cultural intervention, people do not live in bubbles, but it's much more subtle and, I believe, innate than what you think before having children (one data point: my daughter that I swore would never wear pink, actively prefers pink clothes, she wears other colors as well, but given a choice, usually chooses pink and from a really early age)

But there's nothing genetic that determines girls like pink more. It's all social. Your daughter probably saw all the toys and clothes directed at her being pink, all the positive attention she got when she wore that "cute" dress that happened to be pink, and all the little girls her age on television who she looked up to also wearing it.

I meant kids will play with anything. Dolls, trucks, anything their hands can get ahold of. It's only once their parents or society starts subtly and not-so-subtly telling them they should be playing with these toys and not those toys do they start having a noticeable preference. Boys aren't hard-wired to like trucks and girls aren't hard-wired to like EZ Bake Ovens. That's all society.

Yes, kids will play with anything. However, the way they use toys to play will be individual.

My daughter preferred cars and trucks while young (under 4 years). She would cover the garage with blanket for the night, put her small truck to swing etc. The style of play was very different from the way that I saw boys playing with similar toys.

All I'm trying to say is that I was of your same opinion, but facts do not support that opinion in my experience. Of course I have not done an actual controlled experiment, just some observations and little tests along the years. Yes, they will play with anything, but they still show preferences. Are those purely social? I'm not sure.

That said, I am still of the opinion that it is indeed mainly social, but that it is less social than one thinks it is, before.

I'd love to see some actual science about this, got any?

I don't have the original study I read (back in a cognitive development class in college), but I believe this one[0] should suffice. The original was a study that monitored groups of kids playing with toys and found the kids didn't develop a gendered preference until parents began interfering with toy selection. If the parents didn't interfere, they wouldn't develop a gendered preference until school age where they began interacting with other children.

[0]: http://onlinelibrary.wiley.com/doi/10.1111/j.1540-4560.1990....