In Chapter 12, after fighting off some attackers, Hawkeye disagrees with David Gamut that being Christian or not determines whether or not a person will go to heaven or hell. David's response introduces a real religious debate, but it also satirizes Christian missionaries:
I demand your authorities for such an uncharitable assertion (like other advocates of a system, David was not always accurate in his use of terms). Name chapter and verse; in which of the holy books do you find language to support you?
David believes in the "system" he has learned in church. In fact, he is so invested in worshipping according to the conventions taught to him that he sometimes fails to see when it is inappropriate to do so. He takes every possible chance to sing a hymn, even when it might give away the location of the travelers or when everyone would be better served if he were to fight instead. He is well established at this point in the novel as a lovably comedic figure whose religious fervor is impractical if endearing. Cooper interjects here to suggest that David, like other "advocates of a system," sometimes speaks without understanding what he is talking about or why he is using certain terms. Cooper is likely referring to the fact that "biblical authority" has a specific theological meaning, and David is not using it in the correct way. David has clearly heard the term "authority" tossed around and uses it as though he knows what he is talking about.
The satire here is lighthearted. Cooper does not mean to suggest that David is a full-blown hypocrite, but he is poking fun at people who are more interested in the performance of religion than in developing their own belief system based on its core tenets. As a "man without a cross" who nonetheless believes in God, Hawkeye represents a more freeform kind of religion than David practices. Cooper generally seems to hold that Hawkeye is a deeply principled and reflective man who has developed his beliefs through thoughtful introspection rather than by rote. Readers are invited to admire David's enthusiasm but also Hawkeye's critical thinking.