Rather than one factor deciding whether a given profession will trend male or female, it seem far more likely it will be a number of factors. I don't even have to lay them out, just assert that the alternative (there is precisely one factor that determines the gender composition of a given profession) seems almost incomprehensibly improbable. The burden of proof would really be on somebody making the alternative claim since nothing in the real world works that way.

Once you have that, you have some gender distribution of such traits, and even if that gender distribution itself isn't normally distributed (and most gender differences do have that distribution, with different averages and standard deviations for the two genders but broadly normal in both senses), the CLT says that the resulting distribution will be normal.

Digging into the math of the CLT shows the result to be relatively robust, too, as you add more and more factors into the mix. Eventually, with many factors (such as comes up when talking about anything human), you end up with a powerful pull towards the normal distribution that requires some pathological distribution to avoid.

Taleb's "Black Swan" theory, glibly paraphrasing, says that there are more such distributions than people realize, especially when you start using the CLT to gloss over pathological cases that arise in the real world. However, I don't think any such pathology exists today, and the pathology usually claimed ("systematic discrimination") was a lot more plausible before the events of the past 20 years, such as I described in my original post. (The "very strong" force is not something like "the dudes in my comp sci 101 class keep trying to pick me up", it would be more like "women in comp sci classes get death threats" at a minimum. The CLT can be overcome but it takes a lot as you start adding more distributions into the mix.)

To claim that this distribution would not be normal and therefore there should not be outliers would require demonstrating why all of the psychology research, which tends to show normal distributions of all kinds of traits in humanity, is either wrong, or all those normal distributions don't apply to the choice of career path. I don't think this is likely, as the most popular/reasonably explanation of the latter seems to me to be counter to the evidence.

This is a post on a social site; to go beyond this would probably require significant research, assigning numbers, etc. I know I'm handwaving some here, because this just isn't the place to do a full explanation of the CLT, after all. If you're more interested in this subject, I'd have to refer you to a statistics book and some time with a calculator. (I'm serious about that calculator bit, by the way; I have found it's easy to be able to spit out lots of theory without the first clue how it really manifests in the real world. I once did a programming project with Bayesian probabilities, and I found that even though I already knew the theory fairly well, once I actually started testing and computing Bayesian results en masse, I found my intuition was surprisingly poor. The CLT is the same way; you'll be surprised how quickly adding just three or four random variables together gets you to something fairly normal, and how much pathology it takes to prevent that result.)