@yanitza Some of both in this case. Arab legends prior to Islam speak of incursions and trade with the states of 'Ethiopia' wherein the Arab was the master. This concept continued into the Islamic period and did not cease and was strongly held during the Abbasid period. I believe the issue here with a total conquest of Aksum and the interior of Ethiopia, is the time limit. Certainly, Islamic states could conquer the region by say 1200, however, 800 is very early. The Umayyad period covered a relatively short period and its borders had by 767, failed to fully contain the limits to the East, much less conquer the entirety of Ethiopia. For instance, Afghanistan had yet to be conquered until the 860-880s, Ethiopia would be even more difficult to conquer fully.
However, let me give a possible scenario. 745, Yemeni raiders from the Umayyad dominion gather a modest army of Mujahadeen and instead of venturing to the existing fringes of dar al-Islam, they cross the Red Sea to make a gamble in the land of Assab or the coast of Aksum. This army of Yemeni warriors, are able to gain many key victories and create a statelet and dependency of the Umayyad Caliphate, say it is called the Emirate al-Assabiyya or Emirate al-Sudaniyya. This attracts a small number of muhjahid every so often to conduct wars and raids into the region. By the Abbasid period, this state continues to provide slaves and also is bolstered by converts in the Horn of Africa. Thus, through the Abbasid period, the region becomes a minor area of influence, wherein, they receive slaves by force, tribute and trade. However, this will increase the need for a reaction by the interior states of Ethiopia, who will become much more mobilized and sooner in terms of military force. Confederations of Christian and Traditionalists will possibly form to combat the seeming invasion and some states will accept Abbasid dominion and nominally practice Islam. So, if this scenario holds deep into the Abbasid period and other Abbasid calamities are averted, a clear line of soldiers will move to the region and the Abbasid will exert minor influence, thus in say 1100, the majority of Ethiopia could be ruled by Muslim states either under the Abbasid hegemony directly or so influenced, as to be dependent upon trade and goodwill of the hegemony.