Black Israelitism and “Christian Identity” (basically White Israelitism) share many of the same flaws in their thinking.
According to Scripture, if someone cannot trace their entire unbroken father-son genealogy by name, they cannot be considered an Israelite. In Nehemiah’s day, there was a group who could trace their genealogy back to the time of David, over a century before their time. But because at one point there were those who took the genealogy of their wives (Jewesses), and could not trace their father-son line back to Jacob himself, they were counted as polluted, because they “could not show their father’s house, and their seed, whether they were of Israel” (Neh 7).
Also, biblically, circumcision is an inheritance: you receive circumcision from your father, or you are uncircumcised. Ishmael was of the circumcised, but he did not pass it on: his millions of descendants are as uncircumcised as any other, regardless of being of the blood-line of Abraham himself. The same is true of Esau and his descendants. The uncircumcised descendants of any circumcised person are not less uncircumcised because an ancestor was circumcised – as well when those of another nation became circumcised, they were not less circumcised. Indeed, all of Abraham’s servants were circumcised, at the command of God.
Further, the uncircumcised are today commanded not to enter the covenant of circumcision: “Is any called in uncircumcision? let him not be circumcised” 1Cor 7 (no doubt because of the judgement upon the circumcised after they crucified the very one with whom they had made the covenant of circumcision). The circumcised are obviously to keep the covenant they are in, and obviously the remnant, the circumcised who believe, can be grafted into the new covenant: “I say then, Hath God cast away his people? Not so. For I also am an Israelite” Ro 11.
Apart from such ideas as Black or White Israelitism being categorically unbiblical, their arguments trying to connect themselves with Israel are obviously nothing. For example, if someone did prove that all Israelites were black, this would create no connection with anyone today, as there have always been black people who were not Israelites. To say, “If Israelites were black, then black people are Israelites”, is the same as saying, “Jake Jones is black, therefore anyone who is black must be Jake Jones”.