What if the minor shared the desire of the parents and was deemed competent to make an informed decision before the surgery? If the minor, without influence of the parents, doesn't want blood, do you still transfuse in this (life threatening) scenario?
The answer to your question is a resounding YES.
Why? There is no such thing as a "minor who is deemed competent." There are certain areas where minors can make their own medical decisions (e.g., if they are emancipated or pregnant) but that doesn't apply here.
Therefore the parents or guardians make the decision for this minor, period. It doesn't matter what the minor thinks. You do what the parents want.
UNLESS they are choosing to withhold life-saving treatments that are "in the best interest" of the child. Then, the physician acting in patient's "best interest" gets to make that call. This Jehovah's Witness situation is the most common example scenario I've heard of. I don't know what happens if, for example, parents want their otherwise healthy asthmatic kid to NOT get intubated for an acute asthma exacerbation. Presumably the kid would get tubed, right?
In this scenario, I think most doctors taking care of this patient would make an honest effort to avoid transfusion and respect the patient/parent's beliefs about going to hell or whatever the jibber jabber is about them "eating blood."
But in a situation like this it looks like this patient needs some RBCs and quick. If the doc wants to transfuse, the kid gets a transfusion and the parents have no ground to stand on legally or ethically.
One interesting tidbit regarding variability in acceptance of blood products. As said earlier, there is a wide, wide range of what's OK to these patients. Cellsaver, autologous, ANH, plasma, cryo, PLT, albumin, etc. But if they say NO to albumin, then they are a no-go for EPO too, since even though EPO is recombinant it is solubilized in human albumin.