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Mr. Polensky said two students from his religious high school in Dickerson, N.D., have entered training for the priesthood, indicative of “a very strong faith and commitment” among the Catholics he knows.

Membership in the Catholic Church is growing in South America, Africa and Asia, and declining in Europe and the U.S. — but American Catholics said they still expect their children to grow up to be defenders of the faith.

Mr. Polensky is single but said he expects any children he would have to “have some form of faith” and to have that faith in the Catholic Church.

And Ms. Bewley, who is engaged to be married, said she would “certainly hope” that her children would remain in the faith.

“I know it cannot be forced,” she said. “I would try to lead them to that.”

As for Francis’ role in American Catholics’ lives, Erin Walsh said she hopes he “is progressive, open and honest about our failings and opportunities to do better.

“As someone who is Catholic, raising her three kids Catholic, this is an important time for my family,” said Ms. Walsh of El Dorado Hills, Calif.

Though it is far too early for American Catholics to assess Francis’ potential, one D.C. resident might have an edge: Maria Alejandro Albarracim grew up in Buenos Aires, the archdiocese of then-Cardinal Jorge Mario Bergoglio.

“He is a really good man, kind. He would fight so hard against injustice in South America,” Ms. Albarracim said Wednesday as she exited a special Mass at the Cathedral of St. Matthew the Apostle in Northwest Washington.