I live in Turkey currently (American living abroad) and its not at all an "Islamic" country. The people are very tolerant of pretty much everything and most (not all) of the Muslims are extremely liberal/secular when compared to many other Islamic social groups. For example, I've seen Imam's, Christian ministers and Jewish rabbis sharing coffee and conversation with each other and a couple of gay men that had nowhere else to sit in the coffee house. Maybe 20% of the women in my area wear headscarves, no burkas or anything like that... and they'll happily have conversations with women in mini skirts and bikinis (hey its a beach town :) ). Most of the Turks drink alcohol, they have some good beers and almost everyone drinks raki (anise liquor). When the mosque calls for prayers, most of the Muslims around here go about their daily life. Many don't ever attend Mosque.
That being said the AKParty acts much like the GOP in the US. They stay in power because there is a strong Anatolian middle class of conservatives and the AKP constantly make noises to maintain their support. A few months ago they made a lot of noise about outlawing abortion, nothing came of it, but the AKP poll numbers went up. The same for the recent anti-alcohol law... "no shop sales after 10 PM and before 6 AM" but you can still go to restaurants and bars with no problem until 5 AM or whenever they finally close.
While the CHP (the left wing, secularist) party is setting itsself up as the 'secular' alternative to the AKP... they tend to be ultra nationalists. The military has, more than once overthrown the government via a coup and taken control of the country, because the military didn't like the way the government was acting. The CHP tend to be Kemalists (following Ataturks views), but they have a pretty poor track record with other kinds of human rights. Kurds, for example, were treated worse under the CHP and military lead governments than under the AKP. The CHP would have no problem jailing people for speaking against Ataturk or Turkey... and actually kicked an author out of the country for writing a book that included support for the claim that the Ottomans in the beginning off the 20th century were responsible for the Armenian genocide (the nationalist position is that it was a war and lots of people on both sides died).
For some the AKP has provided more freedom. For example, until recently, women were not allowed to wear the headscarf in public institutions (schools, colleges, etc.) and women who kept the headscarf had many fewer job options.
Basically the situation in Turkey is a question of balancing extremism on both sides of governance with the more moderate public. There is no simple answer.