Gender is a messy bloody business. People are really, really invested in the notion that gender differences are hard wired in the brain. I suppose it has a lot to do with identity. Most people consider their gender as a pretty significant portion of their identity. I don't think too many people feel terribly comfortable with the notion that something so central to their being is largely conditional on what the current social dogma says about gender roles.
I know I tend to buy into selective reinforcement type thinking. I'm pretty good at multi-tasking, because I'm female. I'm pretty good at science & maths because I happen to be. I'm tend to analyse relationships and engage in a lot of self reflection because I'm a woman. I tend to drink and swear too much when I go out because.... some other reason. My traits that are generally associated with "female" I attribute to my gender, whilst my traits that are traditionally "male" are for some other reason.
People get very worked up if you suggest that it might not be true that the having or not having of a Y chromosome in and of itself actually affects much about our personalities, our patterns of thought and our entertainment preferences. On the other hand, some other people get equally worked up if you suggest that some of these things might, in fact, have some hard wired component. Very few people seem to take the position that I feel is closest to the truth: that we have absolutely no idea how much, if any, of our gender identity is hard wired.
I think we should proceed on the basis that we have no idea. What would such a strategy involve? It would be pretty straightforward - you'd offer kids toys of all kinds, but not insist that they play with toys of all kinds. If the girl likes "girl" toys, so be it. If the boy likes girl toys, equally cool. If the kid likes a little from column A and a little from column B, also fine. We don't need to bring our kids up gender neutral, we need to bring them up gender accepting.
This is not much of a shift. My kids play with maybe 25% of the toys they have. I have a hard time guessing which things they'll like. So just ignoring gender roles in toy choice is unlikely to make much difference in the hit rate.
We need to proceed on the assumption that we have no idea how strong or weak any given child's capacity for empathy is, and to encourage and assist all of them equally to develop it. We should assume that any given child's language will develop somewhere between 1 and 4 years of age, and not set expectations based on presence or absence of a penis.
However, as they develop empathy, language, a focussed or more multi-tasking approach, a love of sequins or a passion for denim, we should stop comparing this to some arbitrary model of What Boys Do and What Girls Do. We know it's arbitrary, because these models are vastly different across cultures and across time. Pink was a boy's colour in the Western world only a couple of centuries ago. The idea of it being a girl's colour is either non-existent or very recent in most Asian cultures.
What would happen? I don't know. We might find that there are "girl brains" and "boy brains" but that they may not map terribly clearly with Y chromosomes. I think what we would actually find is a spectrum, with most people having attributes traditionally ascribed to both genders. But I really don't know what shape the distribution would be. It might be pretty flat, or it might turn out to have peaks in certain clusters of traits. So what would people call themselves? What would this mean for people who identify as trans gender? I also don't really know. I'd like to think that the idea of gender might become more subtle - not a great big stamp on your forehead that designates you B or G. It might recognise that some people are genuinely neither, or both, and see that as no big deal.
What do we have to lose? My collection of traits still belong to me, regardless of how they came about. I'm still free to identify as female. I might start thinking that perhaps I'm good at multi-tasking because I get bored easily, and so doing more than one thing at a time works for me, rather than because I fail to possess a Y chromosome. I might also expect my sons to be as self-reflective as my daughter, but equally accept that one may be more so than another.
Most shockingly of all, people might manage to find the things they love and excel at, regardless of whether it is a thing expected of their penis-possession status. How is this bad? How does this threaten us?