While it was around, and I was aware of it, I didn't get into AD&D (1e) or any of the boxed versions until college. Then, one of my brother's old friends invited me to join his game, which was just converting from one of the boxed versions to 1e.
That summer, my brother told me about a friend of his who was involved in a game. His friend had mentioned it, bro told him I played, and the friend had invited me. So bro took me to a game, stuck around (since I didn't know anyone there), and even tried to play a game... After that, he never played again ("It's worse than Monopoly. That game never ends!"), but he would drop me off. This continued throughout the summer, until I went back to school.
When I returned, the next summer, something had changed! D&D was "The Devil's Game". It was bad, and evil, an introduction to the occult, and... other bad stuff! Not only my Mom (not sure about my Dad), but also my brother now believed it!
To this day, they still do. I have always wondered what happened, that year while I was away. I have tried to talk to them about it, many times over the years, but the anger the subject generates is so intense that they cannot have a rational (let alone lengthy) discussion about it. Every time I have brought it up, they have gotten angry, and stormed out.
All I know is that I saw a film at church, one night. It was about some young man (whose name I have long forgotten), who was on death row for the murder of his parents, and was talking about why, and all the stuff he had been into...
He had played D&D. He had been into a lot of other things, including going to the local graveyard and entering the crypts to get bones, then trying to cast spells. He stated that, putting together things he got from D&D with things gleaned from other sources, he had found that it worked. He had gotten heavily into the occult, and satanism, and ended up shotgunning his parents while they were sleeping in their bed. The film was shot while he was on death row. He has since been put to death, I heard.
I recall his statement: "D&D is a dangerous game! I think it's very dangerous!" I think that's where a lot of the Anti-D&D hysteria came from (although that's not the only source).
Let's face it; if you believe in the Bible, and take a straight, literal interpretation of it, then there are a lot of things in D&D that ARE offensive, at least at first glance. Spells, divination, necromancy, sorcery, wizardry, etc., etc., ad nauseum, all are directly condemned by the Bible. Demon summoning is right out!
Unfortunately, D&D has all these elements, and even uses them where they don't apply. Clerics, for instance, shouldn't "cast spells", they should "perform miracles". But, nope, the game designers re-use the same mechanic for all classes, instead of Spells for "Mages", Miracles for Divine classes, and "Songs" for Bards...
Some of the recent "additions" to the game won't help, either. Book of Vile Darkness? Book of Erotic Fantasy? I hope no one in my family ever sees any of this... stuff!
Some other fantasy games may get off, easier, just because they're NOT D&D, but many with the same elements won't. While my family always hated any form of RPG ("Weird Stuff" to my Mom - who says the same thing about Star Trek - any version!), they had fewer problems with Sci-Fi or SuperHero RPGs.
Well, I can understand some objections to the game. If you can get someone who objects to sit down and go through the Player's Handbook with you, ask'em to show you what is evil. And then listen with respect, and try to address their concerns. Sometimes, "magic" will be it. Invite'm to play Traveller, or Top Secret, instead...