PVC bags widely used for blood bags and infusions
The main reason is this one: the material must have a certain permeability to oxygen. If not, the blood platelets will not survive. On the other hand, it must not be too permeable to water.
Also, many other conditions must be met in order to store blood and related liquids properly. The bag must be sufficiently heat resistant, so that it can be sterilsed with steam prior to use. The material must not burst in the centrifuge or tear on handling. It must remain undamaged when seriously bent, should be flexible when squeezed and must be translucent to check if the bag is full or contains no layers. Furthermore, the material should be cost efficient and thus relatively easy to fabricate and to weld with the needed tubing.
PVC meets all these quality standards.