The people of Waknuk have suffered a great cataclysmic event—the aptly named Tribulation—which has wrought massive devastation on their society. In the wake of this monumental catastrophe, people try to figure out why such a terrible event occurred. The general conclusion is that it must have been a sign of divine wrath. For some reason, God was angry with the people of Waknuk and subjected them to the Tribulation as punishment.
Under the circumstances, it's considered essential that such a disaster doesn't happen again, and so thoughts turn to how God may be appeased. The simple country folk use a narrow interpretation of the Old Testament to justify the wholesale destruction of anything—animal, vegetable, or mineral—that displays signs of mutations. More disturbingly, this also applies to humans, which is why someone like Sophie, who has six toes, is in serious danger. Effectively, the agrarian folk of Waknuk have decided that the only way to avoid a repeat of the Tribulation is by sacrificing those deemed to be in any way deformed. Although they use the Old Testament to provide a moral justification for what they're doing, in actual fact people in this primitive, superstitious society are behaving more like pagans.