I listen to everything and that doesn't bother my mom. She grew up in New York in the 70's so a majority of her friends are black, whereas she raised us in suburb PA so most of mine and my lil bros friends are white. She never says anything against it.
I can not help but to wonder if they worry about you being ostarcized by friend, family friends and family for not being totally into your culture.
Talk about it with them. Let them know if some of the music makes feel bad. Some rappers bash women and if you are against bashing of women let your mother know that. Get them involved by finding music that would not insult them or you.
There is no such thing as "black music" or "white music". Sure, some genres have more dominant artists of a specific ethnicity but I can name a lot of black rockers (Hendrix for one) and a lot of white or non-black rappers. The color of your skin does not coordinate the taste of your music.