do people with sickle cell anemia produce normal blood cells or abnormal blood cells?

Sickle cell anemia is the result of a genetic mutation in the beta-globin protein of hemoglobin. When the blood is high in oxygen (like in the systemic arteries) the cells behave like normal cells and have no reduction in oxygen carrying capability. Once blood reaches the tissues and oxygen diffuses out of the blood, the oxygen levels are much lower (such as in the venous circulation), which causes the mutant hemoglobin to behave strangely and cause red blood cells to deform to a rigid sickle shape.

These rigid sickle-shaped cells can agglomerate in capillaries and obstruct circulation, where normal red blood cells are much more elastic and can easily deform and squeeze through the narrow capillaries.

Thus the red blood cells of a person with sickle cell disease constantly go between behaving normally under high-oxygen conditions and being pathological under low-oxygen conditions. Without a gene to code for 'normal' hemoglobin, there is no way for a person with sickle cell disease to produce normal red blood cells that do not undergo this deformation.