I think that McBride's main argument is closely tied to his title, and that while most would associate that title with race, McBride intends for his readers to realize--as he did--that in regards to race, religion, and education, humans cannot think everything is either black or white. The mature McBride looks back on his life and realizes that if everybody viewed every area of the human existence clearly (the color of water) and neutrally, then we would have far fewer controversies, whether they be connected to race, religion, etc.
In regards to the second part of your question, McBride has to discuss religion and education because they played just as significant a role in his life as his mixed ethnicity did. While his mother was white, and that certainly created controversy for her and her children, she was also Jewish, and her family would not have approved of her marrying anyone (black or white) who was not Jewish. Similarly, when McBride's mother seeks to get the best education possible for her children, she must combat not only segregation based on race but also differences in religious philosophy with the schools.
Actually, after my teacher and I discussed this, it turned out the true argument is that what happens in the past will reflect in the future. As Ruth is growing up her history reflects her son and her future.