CARLSBAD, Calif. — On a marquee outside and on a banner inside, Pilgrim United Church of Christ proclaims, “All are welcome.” Sustained by the belief that embracing all comers is a living example of Christ’s love, Pilgrim now faces a profound test of faith.

In late January, Mark Pliska, 53, told the congregation here that he had been in prison for molesting children but that he sought a place to worship and liked the atmosphere at Pilgrim.

Mr. Pliska’s request has plunged the close-knit congregation into a painful discussion about applying faith in a difficult real-world situation. Congregants now wonder, are all truly welcome? If they are, how do you ensure the safety of children and the healing of adult survivors of sexual abuse? Can an offender who accepts Christ truly change?

“I think what we have been through is a loss of innocence,” said the Rev. Madison Shockley, Pilgrim’s minister. “People think of church as an idyllic paradise, and I think that is a great part of that loss.”