There are a number of possible morals to be drawn from The Color of Water. One of the most prevalent is the idea that people can overcome their circumstances or other people's prejudices against them. In facing life as a black Jewish family, James and his family members faced all kinds of discrimination and other assumptions about them that they all overcame.
Another moral might be the ability of human beings to deal with tremendous adversity and emerge stronger afterwards. If you read about James' mother's life and her abusive father and the terrible things she endured as a child, it is all the more impressive that she is so amazingly capable and caring for her own family.