Pashe Keqi recalled the day nearly 60 years ago when she decided to become a man. She chopped off her long black curls, traded in her dress for her father’s baggy trousers, armed herself with a hunting rifle and vowed to forsake marriage, children and sex.

For centuries, in the closed-off and conservative society of rural northern Albania, swapping genders was considered a practical solution for a family with a shortage of men. Her father was killed in a blood feud, and there was no male heir. By custom, Ms. Keqi, now 78, took a vow of lifetime virginity. She lived as a man, the new patriarch, with all the swagger and trappings of male authority — including the obligation to avenge her father’s death.