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.
