Most Historians believe them to be Christians who who took on Biblical Old Testament practices, and came to identify as Jews. Steven Kaplan ,G. J. Abbink, Kay K. Shelemay, Taddesse Tamrat and James A. Quirin

http://jic.tau.ac.il/moreshet/reshuma.asp?key=1000104

I hope you can read Hebrew.

Steven Kaplan, On the Changes in the Research of Ethiopian Jewry, Pe'amim 58 (1994), pp. 137–`150. (Hebrew)

Which Ethnicity exactly do you want to know about their relations with? Amharic, Tigre, Tigreyne , Afar,Oromo , Somali or Sidama?