Let us examine what is considered "Black" in the context of this very article. At the very top it states:

"It is also used to categorize a number of diverse populations together based on historical and prehistorical ancestral relationships. Some definitions of the term include only people of relatively recent Sub Saharan African descent (see African diaspora). Among the members of this group, dark skin is most often accompanied by the expression of natural afro-hair texture (although a recent scientific study notes that human skin color diversity is highest in sub-Saharan African populations). Other definitions of the term "black people" extend to other populations characterized by dark skin, including some indigenous to Oceania and Southeast Asia"

This article even mentions Oceanians and Southeast Asians (such as the Great Andamanese, Native Fijians, the Ati,  and the Melanesians) even though these groups genetically have more in common with neighboring Asian populations and are very distant from other people who are considered Black Africans. Ethiopians are black Africans. Some of them have Middle-Eastern ancestry (Ethiopia is a short boat ride from Arabia), but that automatically does not make them an entirely mixed population; nor does it change the fact that their roots are mainly in Africa. Sicilians have some Middle-Eastern ancestry, but they are still considered European. Ancient Romans certainly referred to Ethiopians as black. They used the term "Ethiopian" to describe all Black Africans they came across, regardless of their location outside of East Africa (read this: http://en.wikipedia.org/wiki/Roman_expeditions_to_Sub-Saharan_Africa)

I went to the Beta Israel page and found two very clear references: 

Ephraim Isaac (1974), The Falasha: Black Jews of Ethiopia. Dillard University Scholar Statesman Lecture Series.

Simon D. Messing (1982). The Story of the Falashas "Black Jews of Ethiopia". Brooklyn. ISBN 0-9615946-9-1

Here's more from another article (http://en.wikipedia.org/wiki/Racism_in_Israel#Black_Hebrew_Israelite_immigration)

Rebhun, Uzi, Jews in Israel: contemporary social and cultural patterns

"The Israeli government has airlifted black Ethiopian Jews to Israel and given them citizenship in the same way it has been a haven to Jews oppressed throughout the Middle East and Africa"

"She told RT: “They don't want poor or black children and Depo-Provera gave them the opportunity to have control. If she [a patient] keeps taking an injection every three months, she is not going to have children – you know it is a 100 per cent secure from children I think.”

Hedva says the policy is working – the number of black babies in Israel is decreasing, but there are no official statistics to back up her claim. For community workers and Ethiopian women here, statistics are unnecessary – they feel their reality speaks for itself.

The Health Ministry admits it issues the drug, but says it was never its policy only to administer it to Ethiopian women and reduce the number of black babies in the country."

I would say that makes Ethiopian Jew's a valid part of this article.

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