Other than breeding fish & sheep, I'm no parent. But IMHO, I'd think a compromising approach might help. Downld music they like! And some they wish they had but thought they could never get a hold of. Rare recordings can make a difference, particularly if it's at least with some reasonable listening quality. It doesn't take too much time to downld music specially for the cause.

Also an appreciation of one's parents's music (no matter how out of fad it is) is an art. Take the time to learn about it & this will help you to communicate with your parents. As suggested, this is not easy & needs commitment to learn what was "nice" about the music of "their" day. Understanding their music will help you to communicate your prefered music to them. IMHO But since I'm not a parent, I accept that my advice is that of a person who has only experienced what you have. Understanding other types of music will overall in the long-run help you to communicate with other thoughts & customs, etc. As music is a universal language, but learning how to understand it fully takes time & serious study. Learning more tastes & styles of music will get you far socially. Exceptions for this confused soul called lotr. Just my thoughts!