I come from a deeply Catholic family, but decided to reject that faith and forge my own path, eventually becoming pagan. My entire family (and for practicing Catholics that think birth control is morally wrong, that's a lot of people) felt that I was wrong in doing so, told me so, and tried to convince me to change my mind. When I didn't, they eventually dropped it, accepted who I am, and went on with all our lives. They don't talk religion with me any longer, but are still always happy to see me, and are sure to pour on lots of guilt if I don't come home for Christmas. Likewise, one of my cousins is a lesbian. All of them objected on moral grounds, tried to talk her out of it, etc etc, and once it became clear that she wasn't budging, it was who she was, they dropped it. They do not discuss relationships with her, but are still always happy to see her, and even anyone she happens to be with at the time. They still care about her, even if they disagree with what she is doing.
You can object on moral or religious grounds without hating the person whose behavior you object to.