“How long will Turkey and NATO continue putting up with each other?”
The short answer?
As long as they both exist and Turkey controls the Bosphorus Strait.
If the Triple Entente powers had used common sense post WWI they would have kicked the Turks out of Europe and kept most of Turkey, including the Bosphorus Strait for themselves.
You know, one of the lessons of recent history is that you can hate indigenous peoples all you want, attack them all you want, attrite them all you want, and yet they will remain and you won't be able to control the outcome. And BTW what happened to the Gallopoli campaign. As I recall that brilliant strategem was not a resounding success for ourside.