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.
If you don't feel safe coming out, don't do it. If there is a time that you feel you'll be accepted and they won't panic or freak out on you then go for it. You may want to start off by casually stating your views on the issue to them and not mentioning that you personally are interested in girls. I'm also Christian and there is much proof that God doesn't hold hatred towards gay people (the untranslated Bible doesn't include anything regarding homosexuality). I suggest starting out by casually talking about LGBT issues and eventually, hopefully, your family will start to open their minds.