IOTL, the Turks were lucky enough to invade the Middle East at the time that Sufism and its focus on conversion and assimilation were in vogue, allowing them to integrate into Muslim society easily. What might have happened if, say, the Turks refused to convert, or Sufism was less powerful or nonexistent at the time?
Would the Turks still reach Constantinople? Would they be powerful enough to form an empire of the likes of what they did? Could Tengriism take hold in the Middle East or even Europe?