I come from a Christian background from my mom and Catholic from my dad from the time I knew what homosexuality was I was taught that it was wrong. Because I know how my parents feel I really don't want to even mention that I have a thing for girls. When your father says things like "look at this fruit booty" I find it extremely offensive to hear stuff like that. I have always had a strong support system with my family but if I tell them this I believe they would completely shut me out. I don't want to hide but I really don't want to lose that connection with my family.
It's far easier to hold onto hateful beliefs when it doesn't directly affect you, so don't prejudge how your parents will respond. Even if they react negatively, that is unlikely to last forever. If they can learn to hate, they can be taught to love. Remember, you are a grown woman, and you know yourself best. Have you tried first coming out to your friends or trusted extended family members like cousins? Generally, one goal is to develop a support network so that when you come out to your parents, you can weather any storms that may occur.