It's very interesting that you bring up toys as an example, because it turns out there is quite good evidence that gender toy preferences are partially genetic. Think about this: if toy preference is just a social construction, if we removed all social pressure regarding toy selection, would boys and girls still prefer different toys?

It turns out the answer is yes. In 2002, a (very influential) study was performed on vervet monkeys and found that male vervet monkeys showed significantly greater interest in the masculine toys (i.e. a ball and a police car), and the female vervet monkeys showed significantly greater interest in the feminine toys (a doll and a red pan). There wasn't much difference in preference for the neutral toys.

One study is not enough to show such a trend. So in 2008, the study was repeated a different species of monkey (rehesus) and a different set of toys. The authors found the same results: males preferred stereotypically male toys, and females preferred stereotypically female toys.

So we have two studies in two species of primates that found that males prefer "masculine" toys, and females prefer "feminine" toys. From this, it is fairly plausible that innate differences in toy preference will show up in humans as well.

Sources:

Vervet Study: http://www.ehbonline.org/article/S1090-5138(02)00107-1/fullt...

Rhesus Study: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2583786/

Summary of both studies: http://www.psychologytoday.com/blog/the-scientific-fundament...