Well, Robert Welch (founder of the JBS) thought Ethiopia was a Communist country under Haile Selassie and that the reds controlled it mostly through the Ethiopian Church. Of course, John Birchers can't be taken seriously, but the Church and the Imperial Family were implicated to a certain extent in the proto-leftist civil rights movement.
I suppose the EPRDF doesn't look on islam as equally reactionary?
No, they do.
There is no tolerance for Islmic extremism in Ethiopia and the EPRDF invaded Somalia to forestall what they saw as attempts to radicalize Ethiopian Muslims.
They are also pretty nasty toward Rastafarians as well.