See # 25; Wikipedia (FWIW) seems to link them to Iranians linguistically instead.
Anyway. but the Kurds were separate from various Irani empires from the time of the Seljuk migrations. They remained Sunni as they were not part of the Safavid Empire (the 1700s Iranian empire which forceably converted Iranians to Shia'ism -- though to note that the Safavids family was Persianized Turkic) and they were part of the Ottoman orbit especially in the early 1900s. This was not a problem until the "awakening of nations" in the late 1800s, early 1900s when "nations" felt that they needed ethnically "pure" lands for themselves - this was also the root cause of WWI.