immune system attacks or rejects an imcompatible living organ or tissue?

how about a pacemaker, or boob implant, or knee replacement? It rejects.
That's why after a transplant operation the receiver must take immunosuppressor drugs to stave-off rejection.
It's not a business necessarily of being incompatible, it's merely not the original equipment and wishes all the relief it can get.
There are materials that the body does not authorize as foreign and which do not trigger the immune system. Unfortunately other human tissue is not one of them but some are more compatable.
The immune system only accept or rejects living tissue that is any compatible or non compatitble. This is not restricted to transplants, many auto-immune diseases attack organs/joints, etc. that are already present within the body, i.e. Lupus