Does society underestimate women?

Yes.  The context is female jockeys in horse racing, and so we turn to Alasdair Brown and Fuyu Yang in the Journal of Economic Behavior and Organization:

Highlights

Male and female jockeys compete side-by-side in horse racing.

Betting market prices provide a window onto society’s beliefs about female ability.

Women are slightly underestimated, winning 0.3% more races than the market predicts.

Underestimation is greater in jump racing, where female participation is low.

Here is the paper link, ungated, via Michelle Dawson.

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