I try my best to give everything a chance. I will listen to any and every thing through till the end. I will admit that there are some "categories" I find consistently challenging.
I find most opera difficult. Perhaps the language barrier is to distracting, yet I still don't care for Gilbert & Sullivan despite the fact it filled my house as a child. I don't care for Ragge because it's too repetitive yet I like most minimalist music. I don't care for most Rap except for those rare examples when there is real poetry. Ditto Punk.
Avant Garde/Free Form ala Ornette Coleman, Chicago Art Ensemble etc. require me to be in a certain mind set, when I'm particularly open and not distracted. I have yet to come to the point in my personal development where I can control this state of mind. Often times I will give more opportunity to music that is less accesible to my cultural prejudice. I have found many things in life take many tries before appreciation can be found. Sometimes it works (Scotch Whiskey, coffee, etc.), sometimes it doesn't (fried liver).