I think some of the anxiety would come from being conflict-averse in a polarized environment full of potential misunderstanding. It would be made worse if you had no experience with persons of color.

My (white) wife for example grew up in Berkeley during forced busing and went from being tormented by black girls at the predominantly black grade school she was bussed to, to making friends with them. She would simply have given a matter-of-fact factual explanation and not assumed the black person would be automatically offended. In fact I can't really imagine a black person being offended at such an explanation, or not understanding that a child is a child and simply curious. If I were such a black person I'd go over, smile, introduce myself, and let the child touch my black skin. On the basis that black is beautiful, right?

Of course that's just whitey imagining being black with absolutely no experience of it. Maybe that would be a terrible risk to take, depending on circumstances. The mother could always call the cops, or the kid could pick up on Mom's angst and fear and have a complete meltdown that would be all the black guy's fault somehow. I get that. But someone has to start somewhere. Since the mother is the one with the least downside risk, she should at least give the kid accurate info and not be all red-faced about it.

In such a scenario I'd hope that people would not snatch defeat from the jaws of victory and would push through their discomfort and build bridges and have actual conversations. Keeping such things in the realm of "impolite conversation" helps guarantee it never gets discussed or resolved.

My son at the age of about six asked me one day why his best friend Manesha had brown skin, he said he had asked her and she did not know, I simply said lots of different people have different colour skin depending on what part of the world their ancestors came from and how they had adapted to live in the hot or the cold. He shrugged, said it made sense and never asked again.
I grant you my son may be the exception, this is the same kid who was asking me if the amount the water went up in bath when he got in was the same as the space he took up when he was four, and told me he was an atheist at eight, because god was another made up thing like santa and the tooth fairy to bribe people in to behaving in a certain way.

I never lived in an area where my child would find seeing a person of a different race remarkable.

As a white person from Austria I don't really see a big problem with the child shouting out the skin color of the man. My gut reaction would be smiling at the black person and maybe letting my child know that this is normal. But it also depends on how the child said it. If it was just curiosity and surprise I don't think it's such a big deal.