At least in theory, interspecies blood transfusions would be possible, but only after the donor's blood went through an extraordinarily complicated process to remove all possible antigens and foreign bodies. By the time these blood transfusions became viable enough for the recipient, the cost would be prohibitively expensive compared to traditional human-to-human transfusions. There would still be a high risk of serious illness or even death triggered by a mismatched blood donation.
This is not to say that interspecies blood transfusions have never been attempted. During the late 17th century, long before scientists knew about ABO blood typing, some human patients were subjected to transfusions of sheep's blood in an attempt to restore vitality. A few patients who received these blood transfusions did recover, most likely in spite of the procedure. The rest of the recipients died as a result of severe allergic reactions or other dangerous conditions associated with incompatible blood donations.
The number of deaths caused by interspecies blood transfusions prompted a halt to the dubious process, although other interspecies transplants did continue with variable rates of success. Animal glands in particular were occasionally grafted onto human organs in an effort to bolster the patient's overall vitality or sexual potency or other alleged benefits. Rejection of these grafted glands was a common and often lethal side effect.
The development of the ABO blood typing system in 1907 helped scientists understand the basic difficulty of interspecies blood transfusions. Finding suitable human-to-human donors for rare blood types was already challenging, let alone finding a suitable interspecies donor. Animal blood contained a number of antigens and antibodies which would be instantly attacked by a human's immune system. Even primates with only a 1 percent genetic difference from humans still had too many factors to make the blood transfusions possible.
Considering the difficulty many hospitals and trauma centers face trying to maintain minimal human blood supplies, interspecies blood transfusions would appear to be a potential solution to the problem. Theoretically, blood from slaughtered cows, pigs or chickens could be processed and stored as an alternative blood supply for human patients. There would no longer be a dependence on human blood donations, and a waste product in the meat processing industry could become a life-saving product in the medical world.