I think that shared values and compatible (not necessarily the same or similar) personalities matter more.
That being said, I always think when people ask this question that they have simplified it too much. Being interested in different things isn't the issue, the extent to which each differing interest impacts day to day life is what matters.
So, to take your example of music. If you mean that you would chose Radio One while he would pick and exclusively rock station while you potter around the house then that's not a massive deal. It doesn't really impact much. However, if your interest in a particular genre of music means you regularly go to gigs and festivals of that type, dress in a way that is specific to the music and dabble in an instrument/band related to it while he isn't particularly into music at all then that might matter.
It's the same for sports. I like running whereas my husband prefers the gym but our level of engagement in each is the same. So it works out. If I suddenly became obsessed with running, such as only wanting to go on running holidays, not longer being able to relate to non running friends etc then it could cause a problem because the lack of balance and the amount it impacts our day to day lives.
Anyway, I'm sure you get the point. So assuming values and personality match enough for you to be interested my checklist works like this:
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Are any of their interests something I fundamentally disagree with? E.g directing amateur porn or dog racing.
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Are any of their interests something that would just bore me to death and therefore I couldn't genuinely be supportive when they wanted to talk about/share it. E.g. Football or darts. Same for them, if I'm really into politics and it bored them then it could present an issue if I want to discuss political issues every evening.
3)If 1&2 were NO then it's on to working out compatibility with my own interests in terms of financial and time committments. So, compared to my own interests/ways I like to spend my time are theirs equal, more or less consuming? So long as they evenly match then I'd feel that was okay.
- My final consideration point would be to think about the likelihood of both/either of us outgrowing the interest and if that would matter.
I realize that people can change their interests over time and so this checklist only works for the start of a relationship. So people could say that there is a risk that much later on you could find yourself with clashing interests but that's why I said the most important thing is matched values and personality...thoes should mean that by the time your in a committed relationship you'll take each other into consideration regarding new interests.