Because nobody else is talking to her right now, just be there for her. Take her out, distract her from her problems, be a good sister, help her, communicate daily. This love will be in sharp contrast to the religion she knows. And it will hopefully open the way to more open discussions, she might be a little more receptive in the future.
But what everyone else said too, learn more. Ask her to explain the unexplainable. From the Bible. How come we're allowed blood fractions which come from donations, but aren't allowed to donate? How come we're allowed fractions at all if the Bible specifically condemns blood? Ask her if the gb have said anything about the Australian commission, because obviously there's two sides to every story and you realise the media are biased and wanted the jdub version. Ask her if she can help you understand the overlapping generations thing? Get her on your side, then when she realises it can't be understood because it's all tosh and needs blind faith in the GB, she might realise that you're on to something..
Best of luck!