The thing is, as mum to two boys, the gender stereotypes from the outside world start influencing young children very early indeed.
Humans are very social and relate to peers and older peers very early on, including tv etc.
Baby boys clothes in 2012 were horribly dull and tractor covered in M and s, I vividly remember. The girls had lovely tones of purple and teal and stylish flowers. I found it really hard to find colourful clothes for him. Things have been different for my now 3 yr old.
They pick up on gendered stereotypes quickly. My son was looking at a book with weird stylised animals going into space and labelled the mummies and daddies based on things like eyelashes or broad shoulders (amusingly his own are enormous!)
I noticed birthday gifts for my son's age 4 party were devoid of crafty things, full of fast cars and junior Lego whereas my friend's with girls had umpteen bead threading kits, glittery sticker things etc. It was similar at age 3 parties.
It's no coincidence to me, as a teacher of children with autism, who are sometimes not interested at all in what peers are doing or interested in, that they're more likely to be immune to the sex/gender stereotypes in fashion and interests.
I'm already having the pink is for boys two argument with my 3 yr old, even pointing out his older brother's pink tee shirt!
I think they've found some sex biology differences in things like sight and brain processing of sight; Lisa Mosconi says that on average girls see a wider range of colours that boys and elsewhere I've seen research that says boys react more to fast moving images, but the key thing is that you'll always get outliers, it doesn't mean they're not the sex they are, nor can't study or follow opposite stereotyped pursuits.
Gina Rippon explores this a lot in the gendered brain.