The Byzantines understood Islam as a sort of heresy. Constantine VII (reigned 945-959) in De administrando imperio writes that Muhammed was an epileptic dabbler who misinterpreted Christian and Jewish scripture. When his wealthy wife had had enough of him, to win her back he pretended to have received a message from the angel Gabriel and this was corroborated by an Arian (another sort of heretic).

Constantine goes on to etymologically explain that the Takbir (Allahu akbar) was their way of praying to God and Aphrodite.

And they pray, moreover, to the star of Aphrodite , which they call Koubar, and in their supplication cry out: "Alla wa Koubar", that is, 'God and Aphrodite'. For they call God "Alla", and "wa" they use for the conjunction "and", and they call the star "Koubar", and so they say "Alla wa Koubar".

Anna Komnene (Daughter of Alexios I, 1081-1118), had less flattering things to say:

[Hopefully the Crusaders would] bring dreadful affliction on the barbarian Ishmaelites, who were the slaves of drunkenness and wine and Dionysos. The Ishmaelites are indeed dominated by Dionysos and Eros; they indulge readily in every kind of sexual license, and if they are circumcised in the flesh they are certainly not so in their passions (lol). In fact, the Ishmaelites are nothing more than slaves - trebly slaves - of the vices of Aphrodite. Hence they reverence and worship the figure of Astarte and Ashtaroth, and in their land the figure of the moon and the golden image of Chobar are considered of major importance.

However, after the initial burst of Islamic conquests, the Byzantines found a modus vivendi with the new states and religion. There were Muslim traders in Constantinople and they had a mosque to worship in. Diplomatic letters to the Caliph and the ruler of Egypt were sent with gold seals with the weight of 4 coins while the Pope received seals of 1 or 2. The Byzantines produced a heroic epic about Basil, the Digenis Akritas or "two blood border lord" who was son of an Arabian emir and the daughter of a Greek general. He spent his days fighting the Arabs and converting them to Orthodoxy.

How's that?