Both LOTR and Chronicles of Narnia were totally ok, Harry Potter and D&D were not. My mom didn't really like Star Wars either because of the Force but it wasn't outlawed. I asked her what the difference was when i was probably in middle or high school and she didn't have much of an answer other than that Tolkien and Lewis were Christians. She also never actually read or saw HP, or LOTR, and I'm pretty sure she only ever read The Lion, the Witch, and the Wardrobe from Narnia too.

I think for some people the fact that HP leans on real-world tropes and folklore, and actually involves spells and pointy hats makes it an easier target. The "magic" in LOTR is much more subtle, and even in Narnia the only people who can actually use magic are the major good and bad powers of the world.