I'm a christian and have on occasion fallen into this type of cultish christianity. ime it passed. I'd have to thank God for that... 
That said, I've lost two very close friends to what was essentially cultish christianity. I'm still waiting, decades later, for both or either of them to 'see the light' ie come out of their cultish understanding of God (as I see it).
You say she has eating disorders - which I've come to see as a form of addiction. Addicts notoriously make a cult out of anything - black and white thinking - so something like religion/rigid beliefs is going to draw an addict like a magnet.
imo there's not much you can do. With both the above I voiced my concerns - not even aggressively though possibly with horror - and I was cut out forthwith. The last I heard, one of them was schlepping over to australia at every opportunity, leaving her husband and four SEN kids, to follow this particular branch of christianity, namely a speaker out there who was 'raising people from the dead'. You could argue that she needed raising from the dead: from an abusive husband, hideous battles with various authorities re her kids' education, rumbling debilitating health issues brought on by appalling stress...
What's interesting is that I read the cult's literature this friend was pushing on me, and studied it to try to try to understand it and perhaps reason with her. At that time I had fallen out with God for over 10 years - not least because of the very disordered christian orgs I felt I had been mashed up by: God and I were finished as far as I was concerned. But it was just one scripture from this literature that had a profound impact on me. It was a scripture I had read a hundred times but I saw the meaning of it somehow; and God and I were reconciled. So that's interesting! I didn't subscribe to the cult's interpretation of God but my relationship with God was reignited.
You're going to have to let her go. It's upsetting, you have my sympathy. Be kind to her, if you can. Perhaps see it as her way of trying to bring order into her unmanageable life.