Is this substantively the same as saying they'd rather be subjected to the norms of femininity?
Not really, or at least not exclusively. Olmstead has it more or less right.
That's much better, although it needs some corrections:
A woman2 is someone who has a sense of who most adult females are socially, inferred from their interactions with adult females and how most of them express themselves over the course of their lives, and who feels that they are closer to this than anything else.
We should probably just remove adult altogether. People develop ideas about who girls are, too.
It works as a definition. It also reduces womanhood to a stereotype, and could be considered sexist.
Initially, yeah, it's more or less a stererotype, but in the social psychology sense, and not necessary inaccurate. But it needn't remain that way. If someone transitions, they will start having at least some of the experiences that women do (learning how others treat women, especially if they "pass"). They'll also start learning all the unspoken rules. I've talked to trans men who were shocked to find out how closed off emotionally men can be with each other, or that we're not supposed to talk to each other in public bathrooms, etc.
It's also difficult to see why it's singificant with regards to any policies, especially since it would disqualify many women1.
Of course there's also women3, which is just an umbrella for both, so it's not really disqualifying anyone. This could probably be refined, but I do need to do some work today.
The social policies that follow, at least in the US, are basically non-discrimination policy, which is grounded in the fact that they're a targeted minority. Interestingly, some of those protections are already in place, due to the existence of sex as a protected class. There will presumably be some exceptions, just as there are for all other the others.