My own readings and encounters with Turks suggest that the dominant factor in the national psychology is nationalism, with the particular manifestations: (1) Resentment of the powers to Turkey's north and west for their attempt (as the Turks see it) to stifle the birth of modern Turkey out of the Ottoman implosion, and (2) A mild contempt for their eastern neighbors.
On point (1), I quoted Ottomanist Caroline Finkel here:
"The shadow of Sèvres [i.e. of the humiliating Sèvres treaty of 1920, which left much of Anatolia's fate in the hands of Greece and the League of Nations] hangs over Turkey to this day in the lingering fear that foreign enemies and their collaborators inside Turkey may again seek to divide the state which was defended with such tenacity and at such cost. Attitudes in some quarters of Turkish society to the possibility of entry to the European Union are also colored by the specter of Sèvres, and European intentions are closely scrutinized for signs of duplicity."
Turkish nationalism is pretty close to plain racial pride, tempered somewhat by the universalist legacy of Islam. Part of the problem with the Kurds is the frustration Turks feel at the Kurds' refusal (well, the irredentist ones) to just... be Turkish. Why wouldn't they want to? They're Muslim Anatolians, aren't they?
The sterner kinds of Islam don't have much of a track record among Turks. To see them as a nation of suicide-bombing Talibani is harder than to see them as a nation of hygienic and pacifistic Europeans (which, I'll admit, isn't easy).
The fundamental problem here, as in much of West Asia, is the failure of the modernization project to properly "take," and the flight to religious fantasy as a refuge from that failure. Why didn't modernization "take" in these places, as in Europe or East Asia?
Islam itself may be part of the answer; but there are places with other religious traditions (Burma—Buddhist; sub-Saharan Africa—animist/Christian; etc.) where modernization didn't "take" either.
Lynn and Vanhanen have a mean IQ for Turkey at 101, same as Sweden, so it doesn't look as though that's part of the explanation (though the Lynn-Vanhanen data and methodology have been disputed).
All the old Islamic nations of West Asia and North Africa, when they first stepped out into the slipstream of modernization, dumped Islam and reached for something more promising to grab on to—Socialism, Fascism, Ba'athism, Arab Nationalism, Ataturkism. None of it quite worked out as intended, and educated young people slumped back into Islamism out of despair and cultural humiliation.
Ataturkism was less of a disaster than the other doctrines, though, and I still think it will pull through. Demographics aren't that bad: Birth rate per 1000 & median age are 16.4 & 29. (USA—14.2 & 37, Pakistan—27.5 & 21, Saudi—29.1 & 21.) I remain optimistic about Turkey, though of course a bad economic stall or misjudged foreign military adventure could upend things.