Let's take race out of the equation and just deal with a child who's being disrespectful to an adult in public. Any child I have under my protection will also be privy to discipline should the need arise. I would not hesitate to correct my child when that child is being disrespectful and rude.
And yes, I do have step-children and have disciplined them in public. And yes, those children were of a different race than I was. I won't hesitate to point out that rudeness and being disrespectful crosses all racial lines.