Irrelevant to the individual, but relevant when talking about groups.

For example, upon observing that more women than men tend to take up nursing. Do we conclude that there is a gender bias in healthcare recruitment and a distorted soceital expetation of gender roles, or can it be explained as a consequence of the aggregate personality bias between the sexes resulting in more women choosing that career. The personality science comes in to play when trying to answer that question.

Usually, the correct answer is "insufficient data." The systems are circular and self-reinforcing; what does maternity leave look like in the nursing profession, for example?

All good points. I wasn't actually trying to start a debate about the nursing profession, of course. Just an example of where average personality differences may partially explain observed outcomes.

So they're all irrelevant? That's effectively the same as saying they don't exist in the context of this discussion about their effects.

Why do you think nature is completely irrelevant?

The underlying political philosophy of the US includes the axiom that people are created equal (misunderstanding from original usage of words notwithstanding). If there are differences, they aren't enough to look at a male job candidate and a female job candidate and say "we should definitely hire the man, because his natural advantages will" etc.

The topic is nature vs nature, and how 1 side claims that it's all nurture. You said that nature still exists but is irrelevant, which is effectively the same thing.

What does this have to do with hiring? When did anyone claim choosing one sex over another based on natural sex-based group differences? Of course hiring should be fair and equal opportunity, there's no disagreement there. However if you accept that then you must also agree that both sexes are interchangeable for most jobs and so there's no such thing as a sex imbalance either since anyone can do the job.

If by "sex imbalance" you mean the ratio differential currently exhibited in the workplace, the last piece of the reasoning doesn't follow from the first.

"Both sexes are interchangeable for most jobs" doesn't imply "there's no such thing as a sex imbalance" if people have historically believed both sexes aren't interchangeable for most jobs and workforce gender distribution reflects that history.