Probably not for me to judge, but I actively seek out new bands (as in I've not heard them before) either live or recordings. I'd be lying if I said there were a wide distribution of genres though. But I do try.
I played the violin to a decent standard as a young person and was exposed to a lot of classical and I still love opera and some composers. Then I saw Led Zep play live and my world changed.
When the kids were growing up I played them all sorts of stuff on the basis that it was fine if they didn't like a particular band or genre but I made them articulate why that was the case. I was trying to get them to understand that for something as qualitative as music there is no such thing as good or bad taste just stuff you listen to and stuff you don't..