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The basic timeframe for Arian and Axum, is that during the 4th century that the Ethiopian Church and the Christianization of Axum through Frumentius began (roughly beginning in the 320s). Arius and Frumentius pretty much ran around in the same area of the Levent and Alexandria area, Constantius II is also at this time considered a Arian. We also have the Arian Theophilos the Indian who a few decades laterworked in the area of Ethiopia and the Indian Ocean in spreading the Arian doctrine.
So I feel thats its quite possible that a series of Alternate Historical Events could lead to the conversion of the Axumite and Ethiopian Kingdoms to Arianism.
The POD-
Frumentius becomes a follower of Arian sometime early in his life. (OTL still gets captured by pirates and send to Axum)
Following the First Council of Nicea Arius is sent into exile in remote region of the Sinai Peninsula
Frumentius returns to Alexandria to get permission to convert Axum to Arianism, gets permission from Eusebius of Nicomedia. Establishes Arian Council. King Ezana fully converts to Arianism.
Theophilios in 354 OTL is exiled to Southern Arabia, spreads to the Himyarites and establishes several Churches in Southern Arabia and is invited by King Ezana to establish Churches in Axum, takes Theophilios under his wing to spread the religion more in the area.
Thereon Axum converts to Arianism, and stays like so when the doctrine takes a downturn in the Roman Empire and the rest of the Med. Sea area. I think this could definitly mess around with Islam (Muhammad makes Arianism more poplular in the Egypt, North Africa, Levent, and Persia if you know what I mean....) and define the Byzantine support (or lack of) for Axum.