Islamic State oil is being more or less freely smuggled into Turkey, while foreign Jihadists are moving unhindered through Turkey into Iraq and Syria to join IS.
Kurds, however, are being prevented from moving through Turkey under any circumstances, Humanitarian or otherwise.
Are Erdogan and his party covert Islamic State sympathizers?
I can't say if they are supporting them but they have some common interest.
First, I need to say that states, unlike individuals like you and me, do not have feelings. They have a strategy (usually) and they stick to it. Ethics is not very important. Turkey is simply doing what they think is in their best interests. Their interest is simply self preservation.
My first thought was that ISIS was a threat to Turkey and that they should do something about it. Apparently it isn't. This might change in the future, but for now, the Kurds are more threatening than ISIS for Turkey. There is between 15 to 20% of Kurds in Turkey. Kurds are also a minority in Iran, Iraq, and Syria. Despite the large number of Kurds in the region, they don't have a country. Some groups like the PKK are considered enemies of the Turkish government because they want an independent Kurdistan. Not all Kurdish movements are violent but this uses violence.
South of the Turkish border, there is now an independent Kurdistan in Iraq and Syria (defacto). They are not recognized as independent but Syria and Iraq can't do anything about it right now, so they are considered independent for now. Turkey does not like that. They don't want to have Kurds going south to secure that Kurdish state. They want to avoid doing something that might make the Kurds more threatening inside their own borders or outside.
As for the oil, all countries need oil. Some will buy it from IS like we buy our oil from Saudi Arabia and most of us don't really feel bad about it. Some people are comparing Saudi Arabia to the Islamic state. Saudi Arabian applies a strict sharia that gives very little rights to women. They had several executions in the last weeks. Granted, they don't kill as many people as IS but they act the same way. We consider some countries as allies and some as enemies according to our interests.
To sum it up, no they are not sympathizer of the Islamic State. They are mostly neutral toward them.
According to the Soufan Group, Turkey has in fact up until the recent attack on Sucuk tolerated rather than supported the Islamic state, by keeping their borders open to IS reinforcements and recruits, turning a blind eye towards IS recruitment activity within Turkey, and allowing the sale of IS oil, and preventing the U.S. from attacking them from their air bases.
The reasons are (a) the belief that IS would not attack within Turkey because Turkey is mainly Sunni, and (b) that they were useful for fighting Bashar al Assad's Alawite (on offshoot of Shia) regime.
Interpreting this information myself, hurting the Kurds appears to have been more a desirable side effect rather than the main reason for helping IS. Turkey's fear of Assad would suggest their main worry is Shia influence, and, to that effect, Iran.
This strategy now imploded, as IS mainly fought other rebels in Syria, and now Turkey itself.
