"For outsiders, we see evidence for gender bias: women’s acceptance rates are 71.8% when they use gender neutral profiles, but drop to 62.5% when their gender is identifiable. There is a similar drop for men, but the effect is not as strong."

Yours is a good point, however, that seems to have been missed in the reporting on this study. The men's acceptance rates did also drop (significantly even) when their gender was revealed. So it appears that men might also benefit from having a gender-neutral identity.

[1] - https://peerj.com/preprints/1733v1.pdf