They say Harry Potter promotes a belief in magic and therefore it is satanic because it is un-godly. At school (all-girl catholic convent aaargh!) we were taught that it was in violation of the commandment 'I am the Lord you God, you shall not have strange gods before me' to dabble in anything occult. This meant everything from black masses to reading your horoscope. We weren't allowed to believe in ghosts either, unless it was The Holy Spirit, or Jesus' ma appearing to St. Bernadette and whoever else, and practising magic was about as bad as you could be. It was also in violation to spend more time thinking about your favourite boy-band than you did about god or anything else for that matter like money or sex or the fact that you couldn't wait to get home from school and have a bacon sandwich or something.
Basically if it wasn't rooted in Christianity it was satanic. I haven't read them but I've noticed no real satanic references. Although at one point Professor Snape tells them he can teach them to brew fame and bottle glory and riches. I guess that's kind of Satanic. But there are no baphomets or black masses or orgies or anything.
If JK Rowling is reading this here's a future book title suggestion - "Harry Potter and the Golden Shower Baphomet Orgy".