Thing is, it doesn't matter what you believe in, you are still exercising blind faith. If you believe in science and nothing else, that is still blind faith; science still has more questions than answers, but you believe that eventually science will prove everything - that is FAITH.
At one point we believed that the Earth was flat. How ridiculous does that seem now? At the time it made sense, but were those people deluded? I don't think so. Was there belief based in blind faith? Yes. We can see that now. Science is full of "everything we thought we knew is wrong moments", and there will be more to come. Point is our current collective train of scientific thought could well be deluded.
I believe in science, but who pressed the start button in the first place? For me that was God. Also, I believe that science and curiosity have given us knowledge and abilities that we as a race have no idea how to handle. We need morals and guidance, because we have half a brain cell, and we are dangerous. For me, that comes from Christinaity.
I hate to hear people talking about any belief system as wrong, or delusional. We are ALL working with a belief system that works for us, and we are ALL making leaps of faith, because NONE of it has been proved beyond all reasonable doubt. Not only that, but ee all think we have the truth; we are all, by definition orthadox, we have to be, otherwise what's the point in holding a belief system?
OP, your friend is troubled and looking for peace. Continue to challenge her, and try to get her to accept your challenges. By doing this, and as long as she really, honestly meets your challenges, you will help her to find peace. Don't make it your mission to talk her out of it, but to help her figure out what she trully believes in.