Using the same logic you could say the US is not a Christian nation. It is a secular country with a majority Christian population. Turkey is not an Islamic state like Iran but it is a moslem country.
The difference being that the Turkish constitution was specifically written to exclude it from being a moslem state. The US constitution has no such provision against Christianity.
(Of course I'm going on memory here and will bow to any of our Turkish Freepers input on this. Let me read from post 54 to the end and see if this gets corrected)