Walter M Miller Jr was a Catholic, and it helps to see the book through that particular blend of hopeless original sin and joyful redemption. He, and many of his characters, believed in both. It's a sensitive portrayal of people who are deeply religious for principled reasons, yet don't fall into easy caricature.
It's the only novel that he ever wrote. He published a couple dozen short stories, many of which are worth reading. Several are available here -- https://www.freesfonline.net/authors/Walter%20M._Miller,%20J...
His notes for a "Canticle" sequel were stitched together after his death into "Saint Leibowitz and the Wild Horse Woman," but that's not even a patch on the original. Terry Bisson did much of the work, and I'm sure it was hard. Where "Canticle" is humane and sharp and focused, "Wild Horse Woman" is perfunctory and scattered and meandering.