On any given Sunday at 7:30 a.m., a visitor to Schlitte Boxing & Fitness may find two dozen or so men and women hitting punching bags, cranking out pushups, or congratulating one another after a particularly tough bench press. It’s not CrossFit. It’s Sunday morning worship at Warrior Church.

To the side of the gym, there’s a stack of milk crates that form a makeshift altar. Before the workout starts, Sean Steele, founder of Warrior Church, kicks off the hour with a 15-minute prayer and discussion from a lectionary. Founded in 2017, Warrior Church is one of four—soon to be six—communities aimed at military veterans and others experiencing trauma that help compose the network of St. Isidore Episcopal Church in and around Spring, Texas.

The St. Isidore network also includes—along with a few house churches—Taco Church, where men gather for prayer at Taco Bell, and Coloring Church, dedicated to “dialogue and artistic expression.” But if ...