I do think there are enough substantive differences between the two books so that if someone was going to babble on about witchcraft, they'd have a much better case against Harry Potter than against LOTR.
For starters, none of the humans in LOTR really cast spells. That's the province of the non-human wizards and elves. Tolkein also made it clear that magic was going to leave the world when the wizards and elves did. Men aren't able to use "witchcraft" or become wizards. For the religious folk, its the idea of men consorting with the devil or whomever that makes witchcraft evil. But since men can't use magic in LOTR, that potential criticism isn't applicable.
For instance, in both The Hobbit and LOTR, Bilbo and Frodo both use the Ring to become invisible. In The Hobbit, the dwarves use magical maps and keys to enter the Lonely Mountain. Aragorn uses the Palantir to gain knowledge, which is obviously a magical device. Merry's sword, a Numenorean blade, is able to kill the Witch-King precisely because of magical properties implanted by human smiths. In the Silmarillion, the Numenoreans are obviously great magicians. Many similar examples can be found.
Magic in Tolien's world is not portrayed as being inherently evil. It is merely a tool in itself, capable like most tools of being used for good or evil. Some forms of magic, like the One Ring, are evil of themselves and cannot be used for good. But that is what sets the Ring apart so greatly and why some characters find it hard to believe that it cannot be used against Sauron safely. They would not have this difficulty if all magic was evil and dangerous for men to use.