Acceptance of mythology?

[The Mushroom]

Then don't.

Hehehe! Fat chance!

Alright, we're looking at both books as if they exist in a monotheistic world. That is how Christians view it. As for why LOTR magic is different from HP magic, I'll take it back to my abc's...

(a) It does not have its source in God.

Why not? In a world where humans were created by God, and where some humans have the power to use magic, then surely He created them with that power.

Well, He created human beings with free will. Just because humans have the ability to do something doesn't mean that they should do it or that God would want them to do it. He created humans with free will because if we can't choose disobedience then we can't really choose obedience. But this isn't supposed to be a theological discussion so I'll break off there.
As far as LOTR goes, the powers used for good come from Eru, and the powers used for evil come from Morgoth. But we agreed on that already.
As far as HP goes, all of the magic used seems to come from the same source. The question is where does it come from.
(b) It is given the name of witchcraft, which is clearly condemned in the Bible.

A rose by any other name...

Not exactly. I looked up the word "witchcraft" in the dictionary and the definition there was

the art or practices of a witch; sorcery.

so I looked up "sorcery." The definition there was

the practices of a person who is thought to have supernatural powers granted by evil spirits

And there we find our source. Evil spirits. Demons. Servants of Satan. If we're judging the magic in the two books by the same criteria, then we should consider this magic evil, just as we consider Morgul sorcery evil.
(c) It is often used to a sinful purpose.

So is "magic" in LotR.

Only by the evils of Middle Earth who get their power from Morgoth. Those who get their power from Eru use it for good. The problem is, as I said above, that all magical power in HP comes from the same source and that source is Satan. That would make the magic in HP evil. Sure, they may use it to acheive good ends sometimes, but witchcraft, even "used for good," is still condemned. Disobedience, even if it's whitewashed, will no more "further His will" then disobedience as black as the abyss.

So there ya have it, folks.
Mushie