Why are blood types important in transfusions?

Survival of Cells. Blood type refers to thousands of proteins (antigens) on surface of cell membranes, as recognized by antibody proteins. Abo and rh types were the first 2 & most important (in terms of transfusion reactions) characterized historically, there are hundreds more. Antibodies in the recipient plasma attack donated cells & antibodies in the donor plasma attack recipient’s cells > transfusion reaction.
Hemocoagulation. Giving the wrong blood type to someone can result in destruction of the new blood, a simplified rejection. A recipient b blood type has antibodies against a so if a blood is transfused into the patient, the anti-a will destroy the new a marked blood cells.