To be clear, I am not taking a side on their Jewish status in halacha, but as to whether what they practice and refer to as Judaism is really Jewish enough to be on topic here. Just because a group claims to be practicing Judaism does not meant their claim has legitimacy. Just as Messianic Jews and Black Hebrew Israelites would not be on topic, neither should Beta Israel, if they have different canonical texts and interpretations.
As far as I know Mi Yodeya accepts answers and questions that relate to traditional Judaism. Traditional Judaism (as I define it) means any strand of Judaism that has a longstanding, traceable tradition that goes back into some kind of antiquity.
By this definition I don't consider many strains of Kabbalah to be traditional Judaism as some books and modes of thinking only go back a few hundred years and seem to come out of nowhere. Also by this definition I (and Ovadia Yosef) do not consider Crimean Karaites to be legitimate Jews, as their community was not longstanding and we can't trace its lineage and customs. By this litmus I would also exclude questions or answers about Black Israelites or Messianic Jews as they are new movements that began within the last few centuries. (Technically Messianic Judaism started thousands of years ago but the movement was cut off, all current Messianic Judaisms are not connected to early Messianic movements like Ebionim)
However, this is not the case for Ethiopian Jews. Ethiopian Jews have been around a long time, and were known by various Jewish communities throughout the ages. They have been brought up since Gaonic times, and the Radbaz speaks about them matter of factly even just a few hundred years ago. We as Rabbinic Jews also have a longstanding tradition with Egyptian Karaites, which is why Ovadia Yosef and many other Sephardic posqim treat the Egyptian Karaites very different than those from Crimea or other parts of Europe. We knew of the Egyptian community, we had contact with them, we intermarried with them (as the Cairo geniza proves), so to exclude Karaites or Ethiopians from this website for not being "Jewish enough" seems really problematic.
In short: As long as we are willing to accept traditional questions and answers about Judaism we have to accept that Rabbinic Judaism is not the only traditional type of Judaism that exists. And it is my opinion that all traditional forms of Judaism should be discussed here, even if the questions or answers deviate from Rabbinic Judaism.