Once again, the examples cited do not necessarily validate your argument. Islamic rule in the Caucasus lacked consolidation, in comparison to in the Levant for example. It is therefore not entirely surprising that the region saw little conversion during Arab rule, considering that the Levant itself (quite literally an apex of Caliphal authority in comparison to the peripheral caucus) remained predominately non-Muslim up to the Crusades. Indeed, notable communities of Muslim Armenians and Georgians do exist.
You are not totally incorrect in your perspective, it is true that within many communities (amongst the Greeks), conversion to Islam during the Ottoman Empire was often described as ''Turning Turk.'' Nonetheless, it must be emphasized that many of these communities retained their language and many aspects of their culture, in spite of numerous instances of Turkification. Greco-phonic Muslim communities may not have identified or been identified by their Orthodox peers as Greek, yet that does not negate the clear Greekness of their identity and culture. This discussion is further complicated by the fact that we tend to perceive such matters through the nationalistic lens that independent Greece has historically presented, perpetuating a clear dichotomy between non-Orthodoy and claim to Greekness.
If we are to look at Anatolia specifically, the Greek-American historian Speros Vryonis refers to the Islamisation of the region as a ‘Greek-speaking populace became Muslim (and eventually Turkish-speaking)’; in his seminal piece The Decline of Hellenism and the Process of Islamization in Mediaeval Anatolia from the Eleventh to the Fifteenth Century.
Goddamn I forgot to respond to this.
Okay, so I have still shown that while the Christian Caucasus and Christian near Eastern Churches don't make 1:1 comparisons to Greece, they both are examples of the population largely not converting (the later even reflects in the genetic distinctiveness of Assyrians from "The Genetics of Modern Assyrians and their Relationship to Other People of the Middle East")
Umayyad Anatolian and Europe would have a level of control that ranges between the heavily consolidated Near East and the less consolidated Caucasus, either would still correspond to very little conversion.
Also, the Arabs did try to consolidate later on, even establishing Garrison towns and Arab emirs through and starting before the Abbasid period, we still saw basically no significant conversations.
As for many of those communities retaining their language, while language is a big part of what makes a certain ethnic identity, it isn't universally so. This is especially so given that many Ottoman Turks were dropping the identity of simply Turk and I think more calling themselves something like "Rumi", similar to but different from their word for the Greeks and leaving the proper Turk term to pastorial nomads in the Empire.
A Greek speaking Muslims and Rumi Turk would both speak Greek fluently. And thus speaking Turk wasn't a necessity to ethnically identify with Rumi Turks.
And the Turks and Arabs governed differently. Like with your Caucasus example, centuries of Arab rule still left a clear Armenian and etc majority population regions, while centuries of Safavid rule completely mixed up the population profiles.
So conversions and the like that took place under the Caliphates matter far more in making assumptions than stuff that happened under the Turks. And I guess the Akritas song kinda describes Arab conversions to Orthodoxy so the ethnic barrier to conversion is only so strong but that's mostly Nobel romance and shit.
