WI Ottomans become Greek

Like the Ottomans, the Safavids were a Turkic group, but became Persianized. They are now generally considered to be a Persian dynasty. IOTL thr Ottomans adopted a lot from the Byzantines, but not the language. How do we get an Ottoman empire that would be recognized as Greek Muslim empire, and modern day Greece/turkey as one Greek speaking Muslim nation state?
 
Sounds like you would need a POD in the 15th Century. I'm guessing Religion is a pretty big divisor. Both the Safavids and existing Persians were Muslim while the Greeks were Orthodox compared to Muslim Ottomans. Considering the Ottomans styled themselves as rulers of Rûm (Rome) after their conquest of Constantinople it's not a stretch of the imagination for them to see themselves as Greek but getting the other nations to accept a Muslim state at that stage is harder.
 
We don't get that, as an Ottoman Empire still controlling Greece (the only plausible means of bringing this about) would control a lot more than just Greece.
 
Sounds like you would need a POD in the 15th Century. I'm guessing Religion is a pretty big divisor. Both the Safavids and existing Persians were Muslim while the Greeks were Orthodox compared to Muslim Ottomans. Considering the Ottomans styled themselves as rulers of Rûm (Rome) after their conquest of Constantinople it's not a stretch of the imagination for them to see themselves as Greek but getting the other nations to accept a Muslim state at that stage is harder.

I suspect religion was the decisive factor. But the Safavids were a heretical nominally Shia group, that worshipped Shah Ismail as a god. The Persians were mainstream Sunnis at the time. The Safavids only becamr mainstream Shia after their defeat at Chaldiran. So, there was still a large religious divide between the Safavids and their Persian subjects.
 
It seems to me that the difference is that the Turkic-descended Persian dynasties moved into Persia and then established themselves as full-fledged civilized states, while the Ottoman conquest of Constantinople proceeded the other way around.
 
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