I think it often depends on how broad your cultural horizons are, as to whether you're interested in folk and music. I'm very interested in traditional and roots music, but parents aren't particularly. They do, however, have a couple of Steeleye Span albums, and as a kid, I took it from there, and found out about other folk bands.
However, I do have fairly broad tastes in music, and I'll listen to classical music, pop, jazz, rock and all sorts of wierd rootsy stuff as well (I'm a regular listener to Andy Kershaw's Radio 1 programme in the UK). This broad taste in music and the arts in general, is something my parents encouraged in me.
Incidentally, I'm also fairly young (22). Most of my (similarly aged) friends don't entirely share my passion for folk music, but when presented with it, they do listen, and on the whole like it. Introducing one's friends to folk music, in fact, can be relatively easy. Introducing them to folk dance is another.
I've been involved in organising and performing at some of the ceilidhs that are held at my univresity. And I know few people who've come along to these events and not enjoyed themselves. On the other hand, trying to persuade the same people that morris dancing isn't the most ridiculous thing in the world is usually an up-hill task.