How is it possible that the Ethiopians who claim to be Jews are actually Jewish if their genetic makeup seems to be so different than the rest of the Jewish people?
According to their tradition, they are descended from converts due to an affair with the Queen of Sheba and Solomon. Source So their genetic makeup really has nothing to do with them being Jewish or not (in fact it never does with any Jew!).
R' Moshe Feinstein wrote a letter about it in 1984.
I don't have the time to translate the entire letter, but pretty much he says that the Ethiopians should be accepted with open arms by the Jewish community if they go through an Orthodox conversion out of doubt.