Iranian women are defying the government by pulling off their head scarfs in public, joining a growing protest movement that places them on the front lines of a debate between Iran’s Islamic conservatives and proponents of greater social freedoms.

The demonstrations, which included more than a dozen women on Wednesday, also betray differences between Iranian President Hassan Rouhani, a relative moderate who has courted women’s support, and the country’s hard-liners, who oppose any easing of strictures on the head scarf,...