Perhaps the significance lies in the fact that people feel faith in God is more important than what money can provide them. Perhaps the author is stating that saving a person's soul so he can go to heaven is far more important than feeding him while he's on earth. The lieutenant hates the Church for ignoring the poverty of the people, but the priest believes that it is only through faith that the poor and oppressed ever feel any kind of hope.
We may also sympathize more with the priest because of the methods the lieutenant uses to accomplish his goal. He sets traps for the priest by killing hostages in the villages where the priest has held Mass and by luring him with liquor. In the end, the lieutenant sends the priest before a firing squad. Even though the lieutenant is shown as a basically good man who cares for the poor, no one approves of his methods. How much can he really care about the poor if he's willing to sacrifice innocent villagers in order to catch the priest? The author believes that even though the Church may have failed the people in not providing them with what they need to survive, it would never sacrifice them to achieve their ends.
People also love the fact that the priest is willing to put his life in danger in order to try and save more souls. He knows he will be executed if caught, but he continues with his quest anyway.