At St. Brigid’s National School, a Catholic primary school near Dublin, boys will soon be allowed to wear the green tartan pinafore that was until now the girls’ uniform. Girls will be allowed to wear trousers to class. The school is also making its bathrooms gender-neutral.

The new policy is a response to a student’s discomfort wearing a gender-specific uniform. It comes as Catholic institutions—like others around the world—grapple with society’s increasing questioning of what gender is. Innovations such as St. Brigid’s are...