Assuming they are Jewish by blood, instead of conversion, perhaps either males or females from Israel, many years ago, intermarried with Ethiopians. Therefore, neither the maternal or the paternal line should match. The autosomal DNA would be the way to go, except it is generally good for just hundreds of years of ancestry, not thousands. So, this is a case, where DNA may not help prove. I may be wrong in my understanding, but have read a bunch in past few months (as I had all my lines tested).
Genetically, they are at least partially semetic, if not necessarily Jewish maternally (which is what matters).
But they practice a form of Judaism, and they certainly convert to make it “kosher.”