I have been singing the praises of my new parish ever since I moved to the small Wisconsin town where I live. Here people respond and sing with conviction during the liturgies. They participate as lectors, altar servers and Eucharistic ministers. Our pastor comes from India. He loves his vocation, projects warmth, and is great with kids. He’s everything you want in a parish priest—except I can’t understand a word he says.

I’m not alone. Today around a quarter of Catholic diocesan priests were born outside the U.S., and about...