I wasn't merely arguing that if there were such a large difference everyone would admit it. I was also arguing that if there were such a large difference we'd all know it.

It's not entirely clear that these are two different things. Admitting a highly politically incorrect opinion publicly and admitting it to oneself or one's friends aren't really completely separate. People tend to believe what they profess, and what they hear others profess.

That would have to be either a really really enormous difference between men and women, or a really weird difference -- weird in that whatever it is somehow manages to make a big difference in competence without having any effect on academic performance, test scores, or reported faculty opinions. Which presumably would require it to be quite narrow in scope but, again, really really enormous in size.

I suspect one source of the disagreement between us may be that you're assigning a high predictive ability to academic performance, while I don't even assign it a very high correlation. This may be because my intuition is trained on different academic fields. I don't have any experience with scientific lab managers (the job the study's resumes applied for). I do have experience with programmers and other related fields, mostly below the doctoral level.

And it seems about as obvious to me that there isn't such a difference as that (say) there isn't a difference of 20cm in typical heights between men and women. Not just because if there were then it would be widely admitted (maybe it would, maybe not) but because it would be obvious.

When I first read that I thought: but there is about a 20cm difference in the average heights of men and women! Is gjm arguing the opposite point from what I thought, or maybe being sarcastic?

So I checked the average height differences between the sexes, and the male:female ratio is typically between 1.07-1.09. This translates to 8-15 cm of difference. So while it's not as much as 20cm, it's "only" a 2x difference from my prediction. Maybe I'm just bad at translating what I see into centimeters and this difference is much more obvious to you than it is to me.

But is it really too much to suggest that when the exact same job application gets radically different evaluations depending on whether the candidate's name is "John" or "Jennifer" it's reasonable to take that as strong evidence for bias in favour of men over women that isn't simply a proportionate response to actual differences in competence?

I don't disagree with this. I just think the cultural power of "politically correct" thinking is strong enough to make people ignore truths of the magnitude of this being counterfactually wrong and stick to accepted explanations.