I think music still matters as a major identity-shaping force for some young people, but it is definitely a smaller and smaller number. The most visible group of these is probably the white college age kids who make up the “indie” world.
I recently re-stumbled across this excellent Carl Wilson column in Slate: http://www.slate.com/id/2176187/ which is a response to a Sasha Frere-Jones piece that was basically decrying the loss of miscegenation in music, the mixing of black and white influences. Frere-Jones sees the musical landscape divided into black beat-oriented dance and hip-hop vs. white overly intellectual fey indie rock. Wilson re-contextualizes this divide as rich vs. poor. He sees indie as the music of Richard Florida-esque “knowledge workers in training” and hence “Rather than body-centered, it is bookish and nerdy; rather than being instrumentally or vocally virtuosic, it shows off its chops via its range of allusions and high concepts with the kind of fluency both postmodern pop culture and higher education teach its listeners to admire.”
While I’m not sure about either the race or class specifics, I think this description definitely nails the identity-defining role that indie music plays for one type of contemporary bohemian, i.e. the “knowledge worker in training”. I think exaggerating the difference between music as this kind of cultural identity signifier and music a Major Cultural Influence is a classic example of falling for the baby boomer myth of the over-valorized 60s: ‘back then, man, with Jimi and Janis, music really mattered, man!’