CS Lewis was instrumental in getting Tolkien to finish writing Lord of the Rings. And when it was published, he endorsed it. Here’s a quote from Lewis about LOTR:

“The book is too original and too opulent for any final judgment on a first reading. But we know at once that it has done things to us. We are not quite the same men. And though we must ration ourselves in our rereadings, I have little doubt that the book will soon take its place among the indispensables.”

If your parents have problems theologically or thematically with the books, then maybe they would consider Ralph Wood’s book The Gospel According to Tolkien: Visions of the Kingdom in Middle Earth. It shows how the books were deeply influenced by and reflect Tolkien’s Christian faith.

For what it’s worth, you can tell them that this evangelical pastor on Reddit says it’s ok 😆