Dave and Amy Carson live with their 15-year-old daughter, Olivia, in Glenburn, Maine. Like many small towns across the state, Glenburn, population 4,543, is too small to maintain its own public high school. Instead, the local government gives families the money it would otherwise spend on education and lets them choose a public or private school for their children.

There’s a catch: Maine won’t allow parents to spend taxpayer money on a religious school. Families like the Carsons, who believe a religious school is the best…