Because someone else's blood is foreign to the patient, transfused blood will still be broken down and 'consumed' by the body in a few days. Similarly with organ transplants. Organs from someone else, even though they might be well matched, will be broken down and 'consumed' by the body UNLESS they are organs from your identical twin OR you take anti-rejection drugs. It is only the anti-rejection drugs that keep the organ as an fully functioning organ. No anti-rejection drugs are used for blood transfusions so the body will 'eat' the blood pretty soon.
Lots of issues here. JW's are never afraid to pontificate on things they know nothing about.
Tissue rejection is an immune system response. The immune system recognizes foreign tissue via antigens on the cell membranes, principally the human leukocyte antigen.
This is always an issue with transplanted organs unless as is noted, the donor is an identical sibling.
The transfusion of erythrocytes and/or thrombocytes is much, much simpler because red blood cells and platelets are much, much simpler than liver cells or kidney cells. There are not an infinite number of antigen signatures with blood, there are only a handful.
These antigens are known as A, B, Kell, Rh and a few other minor ones. Blood is typed when it is donated. No anti-rejection drugs are required.
When transfused blood is rejected, it is because it has been mistyped. If you have type AB blood, you can receive blood from any donor, but your blood can only be given to another type AB. If you have type O blood, you can only receive blood from another type O, but your blood can be given to any recipient. Type AB is a universal recipient. Type O is a universal donor.
In its severist form, rejection of a transfusion is called a hemolytic reaction. These are extremely dangerous, but becasue of the great care that is taken with donated blood, these are extremely rare.
This should answer the first issue. Blood that has been properly typed is not rejected and lasts as long in the body of the recipient as the recipient's own blood.
All things eventually wear out though. When red cells become damaged they are flagged by the attachment of antibodies and destroyed by mononuclear phagocytes residing in the liver and spleen. The hemoglobin within these cells is broken down thus:
The iron is stripped off and the globulin chains are catabolized and their components reused. 94% of the hemoglobin molecule is gone at this point. All that's left is "heme." Heme is the porphyrin ring around which the hemoglobin molecule is built. Within the phagocytic cells, heme is converted through a series of steps into free bilirubin which is released into the plasma. Free bilirubin in the blood is absorbed by special cells in the liver.
Within these cells, free bilirubin is conjugated into either glucoronic acid or sulfate. Conjugated bilirubin is secreted by the liver into the bile canaliculus as part of bile and delivered to the duodenum, via the gall bladder where it aids in the emulsification of fats.
This process is not analgous to digestion. The immune system and the digestive system are two entirely different things. If it is a sin against God, then everyone is guilty because this is what happens with our own blood by design.