When my kids were very young (3 years?), they had a hard time telling gender apart, including their own. It may seem absurd to an adult, but from a toddler's point of view, grouping granny/mom/sister as one and grandpa/dad/brother in another is simply not very useful. They have to individually memorize "Yes, mom is a woman, and dad is a man" before they finally understand the concept.

So I don't think social pressure affects choices of play - a toddler will happily play with cars or dolls while they don't even know they're boys/girls.