I have a similar problem myself. When I was younger and growing up an atheist in a heavily Mennonite town, it wasn't easy to find people who were accepting of D&D. If it wasn't considered satanic, it was considered nerdy -- despite the fact that video games had already lost their "for nerds" stigma and board games were perfectly accepted.
Even now, as an adult, it's hard to find a group. I have lots of friends who enjoy board games, but few who might endeavor to try tabletop role playing, and even fewer who would be prepared to DM. Myself, I have little interest in being the DM, mainly because creating stories and worlds isn't my thing (though I'm happy to read the DM guide and study the rules).
Sure, there are local shops that sell D&D stuff, and they have D&D nights, but I don't think I could stand two hours in a room with many of them. The stereotypes still exist partially because it still fits. There are still socially-awkward, insular nerds who lack personal hygiene who are happy to be poster children for their favorite escape. That's not to say they all are like that -- I know at least a few who are normal, every day people -- but there are enough stereotypical dorks that it's hard to find a good group.
I would try to introduce my boardgame-playing friends to D&D, but there's a major hurdle in the way. When I want to get a group together to try out a new board game, all I have to do is pickup the game, explain it to them for 10 minutes, and we can start to play. Even people who aren't normally into board games are willing to give me 10 minutes to explain it and an hour to play. But D&D takes a huge effort to get started. Just to understand the rules takes at least an hour of reading the players handbook, and it's far too much to take in one sitting. People also aren't really used to role playing, so it can be awkward to ease the group into the action. To make matters worse, you need a DM. If you aren't a DM (or don't want to have to take on that role), you're stuck. Perhaps you could bring in a friend, but now you need to bring in somebody outside your social circle, which makes things even more difficult. But probably the biggest hurdle of all is the time: you can't really appreciate what D&D is about until you are a few hours into a session. Even just organizing that big of a block of time can be difficult, but getting skeptics to dedicate that time to something they know little about is nearly impossible.
I know several people who have played tabletop RPGs, and they all did (and still) love them, but finding people to play with is hard and getting others interested is even harder. Some of it is the stigma that still surrounds the game (IMO, largely brought upon gamers by themselves), but a lot of it is the shear difficulty of getting into the game.
What role playing games need is a "gateway game". Boardgames struggled for years to figure out how to get people past Scrabble and Monopoly and into more interesting boardgames. Games like Settlers of Catan and Ticket to Ride have been successful at doing this: they are simple enough to learn and play, but have enough depth and complexity to make players more comfortable with these sorts of games. If there was a roleplaying game simple enough to learn and get started at, without any experienced players involved, then people could try it out with having to jump the huge hurdle of dedication. Think something like "casual games" or the Nintendo Wii, but for roleplaying.
Unfortunately, I think RPGs have one final hurdle to overcome: playing pretend. We all know how to roleplay, because we all did it as kids: we pretended to be adults, playing house, or doctor, or school. Roleplaying was our biggest tool for exploring social interactions as we grew up. And a large part of that is pretending and imagining ourselves as somebody else. But as we grow up, society tells us that's no longer acceptable. But there are exceptions. Reading books, watching movies, and playing video games allow us to sort of live life as somebody else, even if only very abstractly and temporarily. We don't outwardly display it, but inside we consider what it would be like to be the protagonist and what we would do, and that's allowed. Actors are allowed to go one step further and be the ones pretending, but ask any actor what it was like growing up, and you'll hear about how people think actors are silly. Acting is only accepted when you're really good at it (I find the same thing as a singer).
In order to make RPGs socially acceptable, we have to make "playing pretend" acceptable. I think part of that is drawing the distinction between RPGs and LARP -- a lot of people have seen LARP (it's hard to miss when you see it) and associate it with RPGs, but there's obviously some middle-ground between taking on a role and wearing costumes and makeup (N.B.: I'm not saying there's anything wrong with LARP, but it's a big step from what people are used to and what's socially accepted). I think video games have helped with this: the idea of playing as a character isn't so far-fetched anymore. But acting it out in real life still is, and that's the biggest thing I find turns people off from RPGs. Most of the hurdles I mentioned before were technical, but this one is societal, and those are always the hardest to overcome.
Until that happens, even nerds like myself will have trouble getting a group together, leaving it almost impossible to obtain a wider audience.