Turk here throwing my 2 kuruş.
Not to be misunderstood I want to state that I'm a left-leaning atheist Turk living a normal life in Istanbul. You can tell that I'm not a great fan of our government and I hate IS as much as any sane mind would hate them. However I believe our so-much-hated-by-west government does not have much options but to not turn IS into an open enemy. I will give you few interesting facts so bear with me.
We share almost 1000km with a highly unstable region. Not only we live right next to this hell but Turkey itself has a pretty long list of problems of itself in terms of the quality of our democracy. However our economy is doing great job growing at %4-5 every year. And a big part of it is tourism. Istanbul is one of the most visited cities in the world. Moreover Turkey is known for being a tourism hub of Europe.
Having such a long and unstable border, having an ethnic group wanting to secede, having almost half of the population unbelievably unhappy about government makes us a very easy target for IS. This great economy that our government boasts last ten years can blow up in literally one day by IS blowing up few bombs here and there. 35 millions of tourist gone in just one day. So my point is even though we had the most liberal most extreme left-wing government in Turkey, it would be really hard to tell IS to go fuck himself. There are IS militants with Turkish passports. But not because Turkey is a muslim country who supports IS. Quite a lot of IS militant hold European passports as well.
I find the western idea of Turkey supporting IS because it is sunni muslim very silly and very backwards. Supporting and not having firm stance due to certain threats are different things.
As much as Erdogan disguise as a sunni leader and uses his sunni muslim charisma over islamic majority he gives 0 fucks about the IS ideology. He knows very well that it is a monstrosity that should be eliminated. It is just he also doesn't like guys like Assad who could create a rival country in Middle East by having different ideaology than his “mildy islamic democracy model”. What he does is he uses one threat in order to eliminate the other and let the first threat be tackled in the long run by its own natural way. This is somehow also a very good strategy for avoiding confrontation with IS which could literally fuck Turkey in matters of days for the reasons I mentioned.
I feel like somehow Westerners like to think that Turkey is culturally inclined to support IS which is very untrue. Firstly we are not Saudi Arabia. I would urge you to come and visit Turkey, it is a very liberal country. Even the most devout religious Turk has been enjoying living in a democracy somewhat functional with freedom of religion, goods, speech etc for more than 90 years when our founding father Atatürk established it after the dissolution of Ottoman Empire. We don't have laws mandated by religion. I as a woman am not forced to wear veil, in fact I can wear whatever the hell I desire.
Majority of Turkish people(regardless of their religious beliefs) admire Europeans and thier advancement while seeing Arabs and Kurds and all other southerners as inferior due to their uncivilized ways of living. (I know it is bad)
While we are culturally very against IS it is true that as a country we do not have the firm stance against them because of the above reasons. Simply put Turkey is on the very front line if shit hits the fan. We simply can't afford to go into such a war with an enemy that can inflict enormous damage. It is far easier living thousands of kms away from this craziness and tell why Turkey is not doing her fair share.
As much as an anti-government person I don't think a lefty govertnment could do any better.