The Supreme Court Monday ruled that Missouri may not exclude a church school from a program that funds playground resurfacing, finding that discrimination based on “religious identity” violates the First Amendment’s protection for free exercise of religion.

The Missouri Constitution long had forbidden public subsidy, “directly or indirectly, in aid of any church, sect or denomination of religion,” which state courts interpreted as excluding church-run schools from programs like Missouri’s Playground Scrap Tire Surface Material...