MARIETTA, Ga. — William Stocks, a white, Alabama-born, Republican-leaning member of Johnson Ferry Baptist Church, arrived at the tiny apartment of a Syrian refugee family on a Wednesday night after work. He was wearing a green-striped golf shirt and a gentle smile, and he was eager to teach yet another improvised session of English 101.

Mr. Stocks, 23, had recently moved to Georgia from Alabama, states where the governors are, like him, Southern Baptists. They are also among the more than 30 Republican governors who have publicly resisted the federal government’s plan to resettle refugees from war-ravaged Syria, fearing that the refugees might bring terrorism to their states.

To Mr. Stocks, such questions belonged in the realm of politics — and he had not come that evening for political reasons. Rather, he said, he had come as a follower of Christ. “My job is to serve these people,” he said, “because they need to be served.”

And at a time when conservative politicians, many with ties to Christian religious groups, have aggressively sought to keep the Syrian newcomers out of their states, it is conservative people of faith who, in many cases, are serving as their indispensable support system.