I wonder why Rhesus conflict can happen during pregnancy and mother can make antibodies against Rh protein (I think the correct name is D protein), but it doesn't happen if mother has different ABO type than the child?
It happens, but it is very rare.
Anti-A and Anti-B antibodies are IgM type. They do no cross the placenta. Sometimes IgG can be produced and lead to the hemolytic disease of the newborn.
Anti-D antibodies are IgG type and can pass through the placenta.