Though I do wonder why they think that LotR is satanic? Do they mean 'pagan,' or is it the crypto-Catholicism they object to?

I suspect that they are just bad at reading, in this case bad at getting things that are not explictly spelled out. Like someone skimming internet discussion boards before having their morning coffee and accidentally starting a flame war, they only notice some keywords and sort them into their own narrative without considering what those words mean in context, or that they have a context, or that said context might not what they assume it to be. In case of LotR, I bet the keyword is "wizard".