Another aspect of the Biblical blood 'laws' is that they all involved the death of the creature from which the blood came. Only in that way did the blood represent the life of that creature. For example, if a Jew under the Law were to drain a pint of blood from his best bull (while keeping it alive) and bring that blood to the Temple to present as an offering, it would be useless. The Law required the person to put his hand on the head of the sacrificial animal to symbolize that the animal was standing in his place and then the animal had to be slaughtered. Then a sample of the blood was offered in sacrifice.
But blood donation does not involve any loss of life of the person donating. Therefore, the donated blood could not represent any life.
On the other hand, as I understand it, some of the 'minor' fractions used in medicine are derived from animals that have been killed for that purpose. (Correct me if I am wrong about this.) So, what I am thinking is that, in theory, if one is going to use the Law (or even Gen 9) as a basis for one's blood theology, it would be these very fractions that should be forbidden.
Having said that, I am not entirely sure how much animal blood is used nowadays to derive fractions or medicines.