Still, helping migrants is “not a crisis and not a problem for us. It’s a beautiful opportunity to share the Gospel,” says Pastor Rosalio Sosa, who runs 14 shelters in Ciudad Juárez and Palomas, Mexico. Carlos Navarro, a pastor at Iglesia Bautista West Brownsville, adds that many migrants “were, psychologically speaking, tortured”—“they say my country betrayed me, Mexico is not treating me good, the United States is not giving me permission to go inside the country, so I think the only solution is God. . . . People are hungry for God.” Mr. Navarro says his church has served more than 8,000 migrants, and he estimates that more than a third of them accepted Christ. Yet this sort of ministry is controversial among American Christians. A survey by the nonprofit Public Religion Research Institute last year found that 66% of white evangelical Protestants believe “that immigrants are invading the United States,” making them “the only religious group with majority agreement on the question.” The survey also found that 62% of white evangelical Protestants believed that the presence of immigrants increases crime, and 71% see them as a burden on local communities. “Many of our donors were extreme right-wing evangelicals,” Mr. Barberi says. When he began working with migrants, “they were like, ‘Wait—you’re working with illegals?’ ” He estimates that he has lost as much as half of his financial support because of his migrant ministry. Mr. Navarro’s experience is similar: “A lot of conservatives and churches decided to turn away from migrants. . . . Even in the local Hispanic Baptist church, nobody wanted to help us.” He credits the Southern Baptist Texas Convention and the Cooperative Baptist Fellowship for helping fund migrant ministries when others backed away.