As I understand it ( very little) Kurds are muslim, but are considered heretics on all sides.
The majority of Kurds view themselves as descended from the Medes, who along with the Persians made up the Mede/Persian Empire that conquered Babylon.
Unlike the Iranians/Persians who are Shiite, the Kurd are about 98% Sunni Muslim, yet tolerant of other religions.
There’s been a revival of Zoroastrianism among the Kurds. Some say as a result of their reaction to the extremes of ISIS.