Hi,

I think many Jews today claim to be "Ashkenazi" Jews which is think basically means "European Jews"... If you accept that a few Jews fled during the diaspora to Europe, then made a lot of converts or intermarried so thoroughly with the locals as to become almost indistinguishable, then you have your "white" Jews.
Now of course the same thing can happen in Africa, hence the Falashas, Lemba, etc.
The net result is more genetic mixing, even if you accept that predominantly black Israelites fled to Africa, or that "white" tribes fled to Europe.
Note that many people and tribes around the area that once would have identified with being "Israelite" may have adopted or become identified with Islam with the passage of time. Allah or Eloh was the original God of Israel (hence the name Isra - El), and the Koran exhorts them to return to the religion of Abraham and Moses and worship Allah. The only major theological hurdle is them accepting Jesus as a prophet, but of course not as "God in Flesh" - no big thing for people who already had many prophets.
As to black or white, well, even in one tribe both can exist! My own experience echoes H.I.M.'s words race. When I was 9, my mother married a man from Mauritius, and I gained a new extended family. In that family were some people who were very black, with African features, and some that were very white, even with blond hair, and a whole range of people with every variation in-between. I have two step-cousins, two brothers with the same parents. One is very white, freckled, with red hair. The other has black hair and swarthy features, not black, but "olive" perhaps, looking Spanish or southern Italian.
So I see there is just one people, and even a single tribe can have all sorts.

Respect.