Speaking from my experience, some of the people in my church are the biggest Harry Potter fans I know. Lord of the Rings is also on the favourite films list of a lot of the people I know from church as well.
I don't actually personally know any LDS who have decided to prevent their children being exposed to fantasy stuff. Where I am, someone who did do that would be considered to be a little weird, but I don't think they would be confronted about it.
The general consensus as I see it is that provided you only explore fantasy for entertainment purposes it is ok, and generally that is all those kind of things are made for anyway. You can even be quite an obsessive fan, but provided that you only view it as entertainment (and don't let it interfere with your normal course of life). When you start trying to seriously explore magic and suchlike is when it is deemed to become dangerous.