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.
Zoroastrianism would be a step in the right direction.