About Ethiopians: It is a massive Machlokes HaPoskim whether they are Jewish or need Geirus. In the end of the day, everyone seems to hold like R’ Ovadia that we treat them as full-fledged non-Jews until they convert. This isn’t because we don’t believe their history; rather, it’s because if we treated them as Jews (or even Safek Jews), the standard Psak would have to be that we would treat them all as Safek Mamzerim.
You can’t Pasken that someone is not jewish simply because of the ramifications that would occur if they were jewish. And regarding the Mamzer issue there is a Chazakah that a Mamzer whose status is unknown will not pollute the gene pool so there is a limit on how far back research is required.