I can see how the secularists would miss the Christian symbolism in "The Lord of the Rings" books, but not Narnia.
I am not sure what you mean by symbolism. If you mean a one-to-one correspondence between an image in the story and a meaning, then that is definitely not what Tolkien wrote, nor Lewis. Tolkien wrote mythology, or as he liked to call it, faerie.
As he says in the foreword of The Fellowship of the Ring
I cordially dislike allegory in all its manifestations, and always have done so since I grew old and wary enough to detect its presence. I much prefer history, true and feigned, with its varied applicability to the thought and experience of readers. I think that many confuse 'applicability' with 'allegory'; but the one resides in the freedom of the reader, and the other in the purposed domination of the author.
In his review of The Lord of the Rings for the Times, Lewis wrote:
What shows that we are reading myth, not allegory, is that there are no pointers to a specifically theological, or political, or psychological application. A myth points, for each reader, to the realm he lives in most. It is a master key; use it on what door you like.
Lewis and Tolkien shared much in common, including their opinions on fairy-stories. That some commie grade-B actress can interpret Lewis's mythology as anti-religious shows how successful Lewis was in creating faerie. And what better person to play the White Whitch than an atheist. That role required no acting on her part.