I don’t believe it is elitist, or any more snobbish than any other genre of music (I can be pretty snobbish about Springsteen). I think the way to help dispel the impression of elitism is to do what they did back when I was a kid: actually put money into music and arts programs (rather than just building stadiums for the high school football team) so kids can learn at an early age that classical music is for everyone. I also remember that every year a pianist or string quartet came and played for us, which exposed us to something besides just the Ramones and Peter Frampton (I kinda time-stamped myself there).