My parents are also really conservative Christians. It was kind of weird with them.
They didn't bat an eye about Pokemon. Then again we lived in California at the time so they probably knew about it.
We weren't allowed to read Harry Potter for the longest time, though, and I'd wondered why, especially since I saw the books in my dad's bedroom.
Turns out my parents didn't want us to see/read stuff that would scare any of us badly. Which, you know, was a bit understandable considering that I have 4 siblings, three younger than myself, and Harry Potter has some scary stuff.
But then my parents lifted the ban the summer the 7th book came out. All I remember doing that summer was reading/watching Harry Potter. Of course, the youngest sibling got to do that shit right away, but that's always the case.
Still, they didn't have that hangup with Lord of the Rings. I saw all of those before I even read the first Harry Potter book.