There is music for casual background listening, and music that demands my undivided attention. I will actually turn off music I enjoy if my attention must be on other things at the moment. I will also unconsciously tune out background music to focus on other things. If something is important to me (and much music falls into this category), I prefer to focus on it without distraction.
I can relate to this, in the sense that I can't really 'multi-task' when it ties to listening music... REALLY listening to music. If I'm really listening and really want to appreciate, the act of listening itself is what I have to focus 100% on - no other distractions or other things I'm trying to accomplish. Otherwise if, say, I'm doing work while 'listening to music', I may not even notice that 5 songs on my playlist just passed me by, because I'm not focusing on actually paying attention to the music, if that makes sense.
But yeah, focusing solely on music is something I very much enjoy; immersing myself in it. Earlier in my life, I'd spent a lot of my free time doing that; was also a way to wind down. I'd just put some music on and lie on my bed for an hour or two, absorbing it. Nowadays I rarely do that; I'm too preoccupied doing other things, for better or for worse.
One of the best times these days I can actually focus on music is when driving. Which, actually, is kind of scary given all of the above - it means I'm mostly in auto-pilot when driving, then. Which... I guess is the case for most people, so ah well.
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To the OP - I don't think I 'live it' in the sense you're describing, but I'm not idle/casual either. I'm very particular about what I like and why I like it (or don't like it), and what really speaks to me, but I've got several other things in life I'm interested in & focus on, too.