Senior pastor Kenton Beshore said the first sermons on the plight of illegal immigrants didn't go over well with many members of his evangelical church, which sits on a 50-acre campus in Orange County and has a 3,400-seat sanctuary, sports facilities, restaurant and a man-made lake. "We took a hit on it," said Mr. Beshore. "We had people who walked out and whose giving went away." It was part of the reason the church ended 2012 with a $500,000 budget shortfall, he said. But much has changed in the two years since—both at Mr. Beshore's 14,000-member Mariners Church and at...