Yes. Studies show that children, even quite young children including babies, do have lots of racial bias and they also absorb the unconscious racism in the world around them (including from their parents, community etc). It’s inevitable but a lot of harm comes from the idea of pure “color blind” children because adults don’t take the time to explain and contextualize the biases they are absorbing. Not saying it’s easy, but it’s a common refrain.

When a child avoids saying a person’s skin color, they are most likely showing a learned behavior which is to not mention racial differences (since adults find it awkward or it generates some kind of uncomfortable reaction).