Music is one of those things where it can take a little effort to explore and expand your boundaries. Still, in the end while I personally think that's a worthwhile undertaking, the benefits are personal so all I can do is (like you) encourage others to make the effort. It doesn't really affect me at all if someone else doesn't like [insert genre or style or artist here] but I will say that in my experience, it's almost always a positive thing to get into.
I wrote off broad swaths of musical styles when I was younger because I thought I actually had a clue about what was out there. I wrote off country because I'd only listened to a little bit of country and didn't like it. I wrote off house and trance and a lot of other electronic music because I had heard a bit of that and also didn't like it.
But in both cases, I was lucky enough to be exposed to a wider variety thanks to the internet, streaming radio like Shoutcast, and yeah...even a good bit of unauthorized downloading when I was younger and options for discovery weren't as robust. Now I doubt I could bring myself to write off any broad genre if only because I had to reconsider both times I'd done so in the past.