Re Ethiopians, the metzius is that there’s no evidence or reason to suppose they have any Jewish origin at all. Their Bible was identical to the first half of their Xian neighbors’ Bible, and not to any Jewish Tanach. They have no traditions that are Jewish rather than Xian. They have no genetic markers indicating Jewish ancestry. And their own origin story is completely consistent with the beliefs of their Xian neighbors, and completely inconsistent with Jewish tradition. It seems obvious that their ancestors were normal Xians who one day decided that the first half of their Bible made sense and the second half didn’t. Rather like that group in Uganda who have now been “converted” by the Conservatives.
By way of contrast, the Bene Israel of Bombay had very little in the way of Jewish tradition left, but the tiny bits they had were inconsistent with anything around them, and their origin story is plausible and consistent with our traditions. In addition they did not intermarry with their neighbors, or accept converts, and since they did not allow divorcees to remarry they’re not bechezkas mamzerim.