Dr. Seuss:
There was always a Jewish community living in Ethiopia that was in always contact with the Jews in Yemen and Egypt. Occasionally there were issues whether their gittim were valid. Given that a large part of the Ethiopian population are descended from migrants from Yemen, it isn’t surprising some Jews were included since Yemen at the time has Jews. They may have picked up a fair number of gerim at an early date from Christians who realized their religion was a fraud, but there clearly was an initial Jewish core. That is why the gedolim with the most contact with them (Sefardi rabbanim, such as R. Yosef) have not had a problem with their Jewish origins.