Is the ōmukō mostly male because higher voices clash with the actors'? Can women call?

First, what the ōmukō is. The word means the seats at the very back of the theatre, and also the calls that come from there. "Naritaya!" "We've been waiting!" — short cries thrown at the instant of a mie or into the pause of an entrance. They are not heckling but a practice long cultivated between stage and house, carried in part by organised calling societies whose members have trained at it.

With that in place: no rule forbids a woman from calling. It is true that the calling societies have traditionally been run by men, but that is custom rather than prohibition, and instances of women calling are on record.

The explanation that a woman's higher voice clashes with the actors' is often repeated, but it is not an established finding and has the flavour of a reason supplied after the fact. Timing matters far more than pitch. Too early and the call obstructs the play; too late and it falls slack. To land one short carrying cry on exactly the right point is equally difficult for anyone, and gender does not enter into it. The substance of a call is, in the end, the depth of one's understanding of what is happening on stage.