Catherine's claim of no religious undertone is both true and untrue. It's true in that she did not intentionally set out with a particular secular attitude. It's untrue because all such stories ultimately tell the same struggle between opposing moral systems. It's also untrue because it's almost impossible not to let one's upbringing, social norms, and personal philosophies effect such stories. This is not to say she's actually wrong; but that she had some pre-existing ideas which color both her writing and her opinion of it's deeper meanings. And, at the same time, each reader's interpretation is effected by their own world view.

Catherine's primary underlying plot dynamic, however intended or interpreted, is the most-common form of parable.

For those interested in deeper study into this subject, I highly recommend

The Hero with a Thousand Faces
Joseph Campbell, 1949

A good launching point would be the Wikipedia entry for the book.