A better subject would be professional sports. As an example, the NHL has no rule against female players, and the people making the hiring decisions are strongly motivated to hire on merit; if the team doesn't win, the coach is likely to get fired. Nonetheless, there are no female NHL hockey players. In fact, in the whole history of the league, there has only been one (Manon Rheaume) and she did not do well or last long. 
It would be fascinating to read the feminist explanation for this lack.