The thing about the Turkish culture is because of the geographical location, Turkey and in particular Istanbul has always been a melting pot of cultures. Slavic, Romanic, Jewish, Christian, Greek, Turk etc. there's always been all sorts of people living there so the music has influences from all of these places; that is something that distinguishes it from say Iraq or Afghanistan. It's the Bridge between the East and West.
But speaking from a strictly religious viewpoint even, the Book of Dede Korkut is a Turkic folklore passed around all the old Turk states; Kyrghzstan, Turkmenistan, Uzbekistan, Azerbaijain etc. and it's from the first days of when the old nomads adopted Islam; it's all these stories about this old man who'd walk around with a Saz singing stories.
This is a statue of the dude
And for 1000 years maybe, there have been wandering poets called "asiks" (ah-shooks) who would sing about all sorts; God, Work, lost Loves etc. I know Iran have something similar to that.
This is all very real, and very Islamic. There is this tendency to limit Islam to the middle eastern countries. But there are Islamic countries worldwide, Turkey, Malaysia like Il Duce said, even the Uighur state that went Rogue from China recently, many more
And all these countries are operating well within the bounds of Islam - arguably some of them contributed many of the things that are traditional to Islam. When a country is in a dire situation they cling to old traditions, which is arguably why the middle east is so fundamentalist. The West bombs the **** out of it, rapes the land and then asks why they're fundamentalist - cos you ****ed their home land up the arse and the religion is all they have left, thats ****in why derp!! And it bothers me that the World sees the entirety of Islam as fundamentalist and anti-proggressive. When in fact Islam is based on the very ideas of tolerance and progression. Compare it to what the Turks where doing before that - cutting your thriat and drinking it, raping and pillaging villages, wearing wolf skins and engaging in depraved rituals. That's fun and all, dont get me wrong I'd have a blast doing that. But when you look at the bigger picture, Islam has brought Humanity and our understanding of the Universe a long way.
As have Judaism and Christianity.
As have Buddhism, Hinduism.
As have most all religions that teach some decent Universal laws for people to live by.