To clarify, do you mean to ask specifically how tolerant white American children were toward black Americans? The answer will be different if the question is how tolerant African-American children were toward other African-Americans, or how white Canadian children or white British children viewed African-Americans when they grew up. I don't think many historians will want to assume that "children" in your question refers directly to white American children, though the body of your post leans toward that conclusion.

Also, do you have any specific region or class of white Americans in mind when asking this question? Because the answer may vary based on geographical and socioeconomic factors as well.