Parents are to blame though
I strongly disagree - we are not parenting in a vacuum.
When we didn't want to find out the sex of our DC - we faced huge pressure from the rest of the family as they couldn't buy the right colours and toys - apparently buying neutral wasn't possible.
When we bought neutral for DD1 -pfb- on grounds we were having more DC soon - IL went out and bought pink frilly clothes in such quantities it was unbelievable. We got rid of a lot of OTT frilly stuff and dyed the rest - and most agreed the clothes looked better. Friend with red headed DD who didn't want pink due to hair colour had same - DGP buying entire wardrobes in pink - then you are left with do you spend money already tight on more clothes or use them.
Other random people - including other parents also get miffed if a baby isn't dressed to reflect gender - as they then get it wrong - my Mum bought pink blankets to go with our gender neutral clothes. So there is social pressure - and what people buy our DC follow gender lines despite what we say - though my parents try with youngest DD who like "boy" things like cars but they always buy them pink.
It was random teenagers who passed DS pushing pink pushchair with toy in who made nasty girl and gay comments - this happened a few times- that made my DS not want to do it any more despite my reassurances and comments back.
It was DD1 yr 1 teacher who told her maths was a boy subject - we signed up for mathsfactor with Carol Vorderman in response when her maths too a hit.
It was DS teachers who said when he was struggling in certain areas it was because he was a boy - not because he as an individual needed a bit of extra help in those areas.He got the help at home and then did so much better.
All my DC do dance - but they do street and tap with a teacher who focuses on dancing - not like another local school that incorporates a lot of dressing up as princesses.As a result DS isn't only boy though there are more girls still - though it is usually especially the older the girls the only sport/excersies they do.
I got into trouble with another parent when DS insisted her DD lunch box was a boy lunch box.I have no idea why or where he picked that idea up from- and interestingly he wanted that one for his younger sister on a prior shopping trip as apparently such rules do not apply to her.
There are mixed toys in the house - they all play slightly differently with them - but people who come in like GP do make comments and observations which are gendered - and it's not always possible to stop though we do try and counter.
A lot of differences between DD1 and DS that we and others put down to gender have with DD2 proven to be personality much more. So YANBU to think we can't know how much innate differences matter.
I did read that once that research found there were greater differences between individuals than between genders - but can't remember where.