My impression is that the Kurds are disliked and disrespected in Turkey. I was told (by an extremely limited sample) that the Kurds were lazy and dirty. There was no objection to allowing them their own country, but the argument was that it wasn't enough for them, they wanted more. These CHP supporters also felt that AKP Prime Minister Erdogan had handled the situation with the Kurds badly, being to conciliatory. They believed the Kurds were not as they are portrayed in the West.
The sympathetic view of the Kurds from these same CHP supporters was that they aren't given the same opportunity as other Turks, which is responsible for their bad qualities.
On the bus from Istanbul to Ankara, which was headed to the eastern city of Van, a man told me that this was a "Kurdish" bus. He complained about the smell of the bus on multiple occasions. To me, it smelled like any other bus in the world after and eight hour ride... terrible.
This month, while I was in Ankara, violence hit the southeastern portion of the country as about a dozen Kurdish rebels and two Turkish soldiers were killed in clashes. it wasn't an important news event in Turkey. It wasn't even the lead story on the news that day.
The issue with the Kurds gets directly to the heart of what it means to be a Turkish citizen. Can people who aren't ethnic Turks or are non-Muslims be enjoy legal, social, and economic equality as full citizens? It's been an issue that has persisted since the founding of modern Turkey. The inability of the state to allow minority to coexist has resulted not only in the violence from and against Kurds over the past 30 years, but also in the genocide of the Armenians and in other violence against minorities.
Yet, there is a desire among the Turks that I encountered to be perceived as tolerant of minorities. People are free to be who they are, or so the line goes. But the reality is far more complicated.