A child who is obviously not your own, a child who is treated worse than other children in the family

I couldn’t care less (but one must keep up appearances, right?)

With red hair being rare, a child born to non red headed parents was often assumed to be the child of an affair. Thus was treated badly, usually in the form of beatings.

A person or group treated without the favor of birthright.

A stepchild might be singled out for abuse. But a red-headed stepchild (who presumably looks like his or her absent birth-parent) might be abused even more because he or she is so obviously different from the other children.

an unwanted, (ashamed of) child. Less than desired child

Applied to one who does not fit in and is shunned for the differences and/or is bullied at a high degree