AMBRIDGE, Mass. — Three-year-old twins Zyler and Kadyn Sharpe scurried around the boys and girls clothing racks of a narrow consignment store filled with toys. Zyler, wearing rainbow leggings, scrutinized a pair of hot-pink-and-purple sneakers. Kadyn, in a T-Rex shirt, fixated on a musical cube that flashed colorful lights. At a glance, the only discernible difference between these fraternal twins is their hair — Zyler’s is brown and Kadyn’s is blond. Is Zyler a boy or a girl? How about Kadyn? That’s a question their parents, Nate and Julia Sharpe, say only the twins can decide. The Cambridge, Mass., couple...