it seems such an assumption is more than 99.9% likely to be true

I think 99.5% is probably a reasonable upper bound on how confident you should be (with 0.5% of that being a Gettier case). Physical intersexuality of various sorts has an incident of about 1%, I have read, and in the absence of studies on the subject I'm inclined to deploy an ignorance prior about the mature gender identification of a random intersexed person. Garden-variety transfolk only cut this probability from there.

In certain cases, it's evil (i.e. there should be an ethical injunction against it) because, due to corrupted mindware, certain people tend to overdo it (e.g., if they know that black people have a lower average IQ than white people, they'll consider a black person significantly stupider than a white person in the same situation even though the evidence race provides about intelligence is likely almost completely screened off by information about what they say, wear, and do).

Are the specific examples that JulianMorrison gave things that are statistically true about girls versus boys. Is it statistically true that girls don't climb trees? (I'm a girl, and tree climbing is awesome!)

Also, there's a difference between what you're talking about (using probability to predict behaviour when you know nothing else about others) and ways to raise children, since parents in part determine the future behaviour of their children. Even if it is statistically true, right now, that girls don't wear Spider-Man suits as often as boys, and get upset rather than angry, I don't think those states are the ideal world states. Treating your children like these stereotypes are true might be a self fulfilling prophecy.

Note that there are some examples that I think would be true. I do think that, on average, girls are more likely to get upset than angry when in a situation of conflict. But not always: I get upset more often, my brother gets angry, my sister gets angry, my dad gets upset. I do think that the average boy, if given a Barbie, is more likely to re-enact battles with it than dress it. But that doesn't mean it's a good parenting strategy to yell at your son because he's an outlier who likes to dress Barbies. (From a purely predictive view, you could probably make a boy happier by giving him something other than a Barbie for his birthday, but that's if you're not the parent and your actions aren't influencing his future preferences.)

Apply Bayes to making decisions in real life, in ways that the cool people don't? That idea will never fly on LessWrong!

There's not as much reason to pay attention to statistical reasoning when we have insight into causal mechanisms. Particularly when our knowledge of the causal mechanisms suggests that the statistical results are very susceptible to misleading interpretations.

You have an implicit assumption: that there are actions that you can take which assume that gender identity matches body, that do not enforce stereotypes and which cannot be co-opted to enforce stereotypes.

There is strong evidence to suggest that that is not true, within the current social landscape.

1. They might be full blown trans, whether the kind that's so intense it forces people to transition despite all the grief they get, or the kinds that are less intense or more messy (and probably loads more common, like bisexual is more common than gay).

2. They might want to pick and mix their gender presentation or have a non-traditional way of expressing their identity. Like being a "tomboy" or a boy who likes dresses.

3. They will learn to behave in a non-assuming, non-policing way themselves.