Hi Sarah,
It's unfortunate and so debilitating that life can be soooo bloody awful. Especially to the ones we love the most.
Dena hit the nail on the head about the abuse your sister encountered. Sadly, it's a part of our lives that we must each individually face our own nemesis, usually alone, face to face, before we become victorious over it.
There is little you can do, except send light, energy, love, whatever is your recipe for life to her. She has stated very succinctly, her boundaries, her beliefs, and you must respect them, as she is respecting yours.
I will respectfully disagree on one very important issue your sister raised. Your internal perceptions of who you are, CAN and WILL change, if you change your external appearance. There is much said and written in psychology about the congruency of mind and body. It's a very powerful medium. I further disagree you will damage your mind and body, doing what you are doing through transition. If you remain true to yourself, follow the examples of others in taking the professional road to transition, I guarantee you will be a far better person for it.
Your sister needs her space, grant it to her, but leave your door open to welcome her in, once she has battered her nemesis.
Love
Catherine