I don't think a shared taste in music is that important, or at all, in a relationship but this is the premise of aptly named Tastebuds[1], a dating app based around favorite music. You can import your listening data from Last.fm and Spotify.
So, no music taste isn't ultimate be-all-and-end-all factor but for some it can be very important!
Tastebuds seems only to have a facebook login - hm, not everyone uses FB! Strange that they don't have a Spotify login, probably the same issues that other apps face when they start to store Spotify data.
Spotify doesn't have its claws in real-life gatherings yet, but they might have something with their music (personality) and podcasts (interests, affiliations) data.
Certain genres and scenes are also linked to demographics and lifestyles (e.g. hyperpop being very queer leaning, chiptunes being nerdy, punk being political, bassline and techno being linked to the underground rave scene, etc...)
Also if one of your favourite things is going to gigs and festivals, producing music, or following it, having crossover in taste means being able to share a passion.
A large part of my relationship with my partner is listening to music, either at home on the hi-fi, or at events. If we didn't have a decent amount of crossover, this wouldn't really work.
Having exactly the same taste is probably not so great as I think the differences and gaps are a great space to grow and discover.
I think partly it's just familiarity. There are plenty of "classics" I didn't really like when they came out but now they bring a feeling of nostalgia so even though they weren't "me" back then, for some reason they now feel like part of me, my history, my experience.
I have a largish group of friends that I met through similar tastes in music and being "neighbours" on last.fm.
Slightly off-topic, but originally I had planned to organically grow the playlist count by allowing users to login with their Spotify account and reading their playlists. I even made a prototype...but turns out Spotify only allows working with user data once you have your API quota extended, which seemed like quite the undertaking.
I even went as far as setting a second developer account to have a larger limit ;)
I also did a writeup[1] on lessons learnt in case someone is interested in rinsing and repeating on this idea.
[0] true story, multiple times
Interestingly I found a lot of new music that way and also found other music directions that suddenly interested me.
Thinking this a little further, it provides the perfekt basis for a dating application. Music is a very personally representation of oneself and if you find someone who has the same muscial taste, you already have a common basis for communication.
Obviously this never made it past developer status since Spotify does not like third party apps storing their data (i.e. playlists of other people). You can use the data but not store it or analyse it.
It made me think that Spotify should build a dating app since they would have no interest in keeping you in their dating app as thats not their main business, unlike other dating platforms that have little interest in losing their customers.