I like to make a distinction between playing music and talking about it. When people ask me what kind of music I play, I usually say "mostly traditional music" because I also play jazz, rock, pop, show tunes, medieval, and whatever else strikes my fancy. Most musicians I know enjoy and play a variety of genres and styles. I think that part of the traditions I'm most familiar with has always been using whatever music crosses your path and playing it however you play music. Most musicians are steeped in at least one musical style and that style will come out in their music, no matter the repertoire. A classical musician can make almost anything sound classical and a folk musician can find folky touches to incorporate into music that wouldn't usually be considered folk.

When talking about music, on the other hand, it is nice to have more clear distinctions. So I would hesitate to say that someone who is following a long tradition of playing non-traditional music is a traditional musician or is playing traditionally. In a discussion of folk music, "traditional music" should have a more specific meaning. It gets impossible to keep track of what people are talking about otherwise.

John