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Earlier in the day, association director Bob Lowman said, a Muslim family had walked past.

“God bless you,” Mr. Lowman told them.

“God bless you,” a woman from the family replied. “And Allah bless you.”

“We had another lady come by, and we gave her water and the Gospel of John,” said Mr. Lowman, 51. “She said, ‘Thank you.’ I said, ‘For the water?’

“She said, ‘No. Thank you for not telling me I am going to hell.’”

Back at the convention center prayer room, a delegate who declined to give her name — she works for the federal government — entered, sat down and thumbed her smartphone.

“This is great, a quiet place, all I need,” she said. “I was raised Catholic, but I don’t practice the faith. God is God. That’s it. The distraction of ‘my God is better than your God’ isn’t good.

“God is where you find him or her. I came in here to get in touch with that.”

The woman’s phone buzzed. She returned to checking her email.