Answer:
   
   The answer depends on where you are talking about. First, note that
   the term "Black Hebrews" is not appreciated (although used) by most
   individuals in such communiites. The term is used only because they
   were branded with the name by the predominantly White media some
   decades ago. The problems with the term is that it normalizes the
   "Whiteness" of the Jewish/Hebrew people. The groups actually refer to
   themselves as "Hebrews", "Israelites" and in many cases,
   "Hebrew-Israelites."
     * In Israel:
       First, note that there are many "black" Jews in Israel that are
       properly affiliated with Judaism--in all movements--including
       Orthodoxy. Many were converted generations ago and their
       descendants deserve the same credibility given to any child born
       of a Jewish mother-converted or otherwise. Others have come from
       African communities who have practiced Judaism for ages. In the
       eyes of Judaism, it is whether you are a Jew, and not your skin
       color, that matters.
       However, in Israel, there are groups calling themselves "Black
       Hebrews" that are African Americans, not Ethiopian Jews, who moved
       to Israel in late 60's-early-70's. There is a wide variety of
       "Black Hebrew" practices in Israel. Some are Torah Israelites,
       some ascribe to "the whole bible", and some claim they are Torah
       based. Some of the misunderstandings about the nature of these
       groups arises from the particularity of African-American religious
       sensibilities, which themselves arise out of fundamentally
       different experiences than those of any other American group.
       Thus, the categorical boundaries that apply to Euro-Americans
       (i.e., Christian or Jew, Muslim or Christian) cannot be so easily
       applied to the African-American religious traditions. This
       partially explains why these groups identify with ancient culture
       and not the religion of Judaism.
       Some groups called "Black Hebrew" Israel (but which are really
       not) practice a fundamentalist form of Christianity, but do not
       consider themselves Christians or Jews, but Hebrews, "true"
       decendants of the "Hebrew race". For example, they fast on
       Shabbat, and are strict vegetarians, to name a couple of examples.
       They have a large community in Dimona in the Negev, and they often
       hold jazz concerts throughout the country. They recently received
       permanent residency status, and official citizenship is soon to
       follow.
       Many African American Hebrews practice Kashruth, circumcise their
       male children, observe Shabbat, as well as many other customs.
       These customs were passed down from their grandparents, although
       they may not be understood as Jewish at the time. Some in this
       group grew up practicing all forms of Christianity, some have
       given such practices up completely, others have mixed Christian
       practices with Jewish custom. Such African American Hebrew
       Israelites identify with ancient culture and not the religion of
       Judaism
     * In the United States:
       Note that according to the Council of Jewish Federations, 2.2% of
       America's 5.5 million Jews identify themselves as black. There are
       many observant Black Jews living within American communities in
       all movements--including Orthodoxy. Many African-Americans were
       converted generations ago and their descendants deserve the same
       credibility given to any child born of a Jewish mother-converted
       or otherwise. In the eyes of Judaism, it is whether you are a Jew,
       and not your skin color, that matters.
       In the United States, some groups of Black Jews use the term
       "black hebrews". The name is an artifact of the times when white
       synagogues refused to accept them as Jews.