From what I gather (from here and elsewhere), the group is a Christian group which accepts Jesus as a messianic figure and which considers itself to be the only valid set of descendants from the ancient tribal sons of Jacob. They have no connection to Judaism that modern Judaism would accept (without matrilineal descent or an approved process of conversion) and claim that the proof of their connection is that black people found world-wide suffer the curses in Leviticus 26 and Deuteronomy 28, and this defines who is a proper "Israelite". They deny, then that modern Judaism has anything to do with who Israelites are or that anyone else who isn't black can claim any connection.
Because they lack any actual familial tradition of connection, and do not practice Judaism, they are not accepted as Jews.