AHC: Have the a majority of Greek speakers become muslim
AHC: Have the Byzantines be succeded by a Islamic Greek speaking empire(ATL Greek Ottomans)
How would Greece becoming Islamic affect the perception of ancient Greece in the West, the Islamic world and beyond?
I am not sure if these two are meant to be in the same timeline? Also, in the heading, you write "Greece", although in the text you talk about Greek speakers in general. How do you define "Greece". Remember, until the wars between Greece and Turkey after WW1, a lot of Greeks lived in Anatolia and Istanbul/Constantinople, so I assume that in the ATL you are looking for, "Greece" means a larger area than the current state of Greece. If so, a majority of Greek-speaking muslims do not necessarily have to mean a majority of them speaking Greek in the areas that in OTL are currently parts of Greece.
So, how could a majority of Greek-speakers become Muslims?
Hellenization of the Ottoman elite, followed by a gradual change of language among the Turkish population would increase the Greek-speaking population.
With an early Arab conquest of Constantinople, Islam might even develop differently, if it falls under the influence of Greek philiosophy.
Islamic Greece happens if the Ottomans don't conquer Egypt in the 16th century. Up to that point the Ottoman state was Anatolia and Rumelia. It was the conquest of Arab lands that spread the empire too thin to absorb the Greeks fully. In Anatolia though the majority did convert over the centuries.
Although large parts of Anatolia were conquered by Turks centuries before they conquered the areas that are currently parts of Greece. Besides, before WW1 and the expulsion/genocide against Armenians and Greeks, the non-Muslim population of Anatolia was much larger than today. Large parts of the coast were Greek-speaking (which in most cases probably meant that they were Christians).