Q. Is there any truth in saying that Joseph took Mary and the young child to Egypt, since Herod was searching for him, because they would have been able to fit in there without being detected, based on the color of their skin? Some people think so.
I think the main reason that Joseph and Mary went to Egypt as a place where Jesus would be safe from Herod is that there was already a large Jewish community there, particularly in the city of Alexandria, and so they would have been able to find housing and work within that community, or at least with its help, for as long as they needed to stay. (Please see my fuller comments in this post: Where did Jesus live in Egypt?)
In terms of skin color, really anyone who went to Egypt at this time would have “fit in,” because people had long been coming there from Sub-Saharan Africa, farther west in northern Africa, and the Middle East, and so it was a place where people of many different skin colors lived together and interacted. The Egyptians, really like all ethnic groups, had a variety of skin tones themselves. So Joseph, Mary, and Jesus, whatever their own skin color was, would have blended in not because they looked like everybody else, but because nobody looked quite like anybody else, and so nobody stood out.
(As for what skin tone Joseph, Mary, and Jesus might actually have had, for one possibility, please see the icon I use as an illustration for this post: How long did Jesus live in Egypt? But of course no one knows for certain. First-century Jews themselves had a variety of skin tones. But I think this is good; we can all imagine Jesus looking a lot like us, and this helps us understand that he came to this world and became human like us in order to be our Savior.)