I’m not sure how Islam fits into the whole conflict since Christians run both countries.
Hardly. The dictator of Eritrea runs Eritrea.
Ethiopia is officially secular, which means the leadership isn’t anything in particular. Carving new chunks out of Ethiopia has been an ongoing process.
[snip] Orthodox Christians account for about 43% of the population, while approximately 33% are Muslims. Protestant Christianity arrived in the late 19th century and has expanded rapidly in recent decades to account for an estimated 20% of the population. [/snip]