Music is a huge part of my life too. I am a singer and very passionate about the music I enjoy. I am lucky enough to be dating someone who shares my tastes in music, and we can listen to and discuss music for hours.
I was involved with someone for almost 2 years who disliked my music and had no interest in my singing, despite being a musician himself. He liked completely different music and looked for vastly different qualities in his music. At first this did not bother me too much. We had a "live and let live" attitude like Trippin, but what eventually got to me was this: I'd never be able to go to an opera or metal concert with him. He'd never enjoy or appreciate going dancing at a goth club. All these things I'd have to do without him. And he'd never have me accompanying him to a drum and bass party or an underground rave because that just wasn't my scene. Music was a big part of both our lives, our social lives revolved vastly around the music scenes we were involved in, and having such differing tastes meant that we would always be in separate crowds, never being able to enjoy the mutual appreciation of an art.
In the end we broke up (not because of the music issue), and though we are still friends I realised that in the end the enforced separation by our different tastes would have driven an even deeper wedge between us.
So yes, my partner's taste in music is important to me.