Male voice choirs for one.

Ceoltas and the Gaelic Mod have separate classes for male and female singing regardless of the register, don't they?

The Baccu Ber in France has only boys and young men.

Javanese Bedoyo and Srimpi is for girls only.

There are loads more traditional dances which have a gender bias but have named a few actual traditions rather than hypothetical ones I don't have to search out any more.