They are happy enough with Erdogan, he is an Islamist.
If he was of the Ataturk mold, a secular moderate, they would want to take him out.
One of the biggest problems I have in the Mideast is defining the players. Sometimes they seem all over the board.
I know at one time Erdogans son Bilal who runs a major smuggling op just South of Turkey was selling or middle-manning isis oil. Now isis is raping and pillaging in Turkey.I can never keep up with the players who is who, what side they are on, etc.