The thing I've been told about eating disorders is that people never really get over them, they just learn to manage them.
Depending on what triggers your sisters ED and how she's managing it, really depends on how you should handle it. Maybe go to her doctor and ask the best way you should be approaching this situation.
But, I don't think you should see it as a vegetarian/vegan/omnivore/meateater issue. It's a general food issue. If it were me, I'd emphasise the good and minimise the bad. So, embracing the food I could eat and that which I couldn't, I just wouldn't mention at least around her.
I'm in grad school for clinical psychology and specialize in eating disorders/body image issues. It is true that what you eat could serve as a trigger for your sister's ED, but this would be true regardless of whether you are vegetarian, vegan, or whether you subsist solely on potato chips and cheese fries.
It's important for you to talk to your sister to find out what her triggers are. You may find out that it's helpful if you don't eat in front of her, especially if you tend to eat things like low-fat salads and she still needs to put on weight. You don't discuss the nature of her ED, but if she is a very low-weight person with anorexia, she will likely struggle with the fact that you can get away with eating kale and spinach and things like that while it appears that the whole world is trying to "make her fat." (This is what it often feels like for people in recovery from anorexia)
On the other hand, if she has trouble with binge eating, you may find that she is uncomfortable when you eat snack foods around her, or even uncomfortable with having certain foods in the house at all.
The important thing is to talk to your sister (actually, your whole family should do this) and find out what her triggers are, so that you can avoid them where possible.
Parents can be quite influential, when inflicting their own views on their family. If you break from the mould, even amicably,you can still retain psychological fears and guilts. Which may mean that, although it is perfectly safe to jump directly to veganism (and many do), it may be best to do it in stages over a time to satisfy subconscious worries.
ED can arise from such subconscious conflicts, too - maybe your sister deep down would prefer a vegetarian diet, even though she may not realize it.
A forum community dedicated to vegetarian, vegans, and vegetable enthusiasts. Come join the discussion about agriculture, preparation, cooking, recipes, scales, reviews, accessories, classifieds, and more!