I would respect the wishes of anyone regarding their own body. It's not my place.
It's not your place to care for the people you love? Imagine your 18 year old daughter suffered from anorexia nervosa. It has a death rate approaching 20% and leaves survivors with a lifetime of frailty through bone loss, reduced heart capacity and organ damage. Would you really respect her wishes regarding her own body? Wouldn't you urge her to get professional medical attention? Maybe even have her sectioned as a drastic last resort if you felt her life was in danger?
Now imagine that same daughter wants to refuse a lifesaving transfusion. Why is this situation any different? If the only reason you can come up with is a religious one please explain why that matters.