Thank you for those links earlier, BetsyM00, I was on my phone and didn't have the references to hand.
It's not always productive to start trading links to papers online, I know. I did smile wryly at illegitimatemortificado pointing out above that small data samples are not a barrier to people finding studies on "brain sex" compelling, if they are so inclined.
However, as I said above, if we're starting to change data collection methods and policy and we don't know the answer to the question "what effect will changing the defining characteristic of "woman" from one based on sex to one based on gender identity have?", then that's simply not good enough.
I think that gender identity is biological/has a biological component - this is an interesting one. I can very well believe that it does. In the sense that there is likely some combination of genes or hormones or other factor that we don't fully understand yet that causes people to develop gender dysphoria. We also need to understand the links/overlap/correlation to autism, quite urgently.
What that doesn't mean is that the dysphoric person becomes the opposite sex. That's magical thinking. And in the end, I believe it's unhelpful, because that person is always going to "fail" - it's irresponsible to encourage people to believe that they can be something they're not. Look at poor Jazz Jennings, for example.
And it also doesn't explain autogynephilia, which does exist and comes under the umbrella of trans these days. I am completely unwilling to make any accommodations at all to allow fetishists to use female spaces for validation. And yes, I have encountered the mythical transwoman in the bathroom making me uncomfortable. This person was 6 foot 4, drunk at 11am, extremely angry and banging on a toilet cubicle door at a terrified woman within. I don't by any means think that this is typical, but please don't tell me it never happens, because it does.