Turkey has gone so far as to outlaw Kurdish language. They recently leveled most of a Kurdish city that had become restive. Turkey correctly views Kurds as a threat to their power in the hinterlands of Anatolia. In fact all of the states with large Kurdish populations - Iraq, Syria, Turkey & Iran - have fought against them, and all (but perhaps Iran) actually got paid by the US to do it. Turkey was the largest recipient of US aid under Clinton when they were taking their shot at them. I'm pretty sure this was purely a "stabilization" policy, but we can't ignore the reality of oil and planned pipelines that are present in the Kurdish regions.
As far as Turkey is concerned, I think they followed a similar (if less extreme) policy to their approach to the Armenians. Turkey controls their heritage - they own Mt. Ararat and ancient Armenian Christian towns are crumbling under possession of Turkey. It should not pass without comment that Kurds try desperately to join Turkish mainstream (many were killed at a peace rally they planned in Ankara) and it is not unreasonable to think that a Detente between Turkey and the Kurds could be highly stabilizing, but somehow I doubt that is in the works. I do think that in Syria and Iraq they are or will be assets to stabilization
As it regards Trump - he can't do worse than Bill Clinton to the Kurds, but he can make US policy worse. It is a little insane that the US backed the Kurds in Syria while it backed Saudi in Yemen against the Houthis, since in both cases, these minorities and their pluralist tactics are probably the best hope for secular consensus-building.