Shinko Inori is not a man of faith. He knows that praying is worthless, and that God doesn't exist. He knows that there are logical explanations for everything.
Even getting sent to another world, where his prayers come true and elves are real, doesn't prove anything about God existing in his eyes; all it proves is that he's extremely unlucky.
But despite knowing that religion is ultimately false, in order to survive the new world and go back home, he does something rather strange; he becomes a priest.