The Kurds are an ethnicity, not a religion, and they are not monochromatic. Their history is long, often violent, and rocky as they contended with Persians, Arabs, Turks, and others.
Kurds very rarely “contended” with Persians. Remember that Persians are less than half of the population of Iran, the rest are other Iranian groups (including Kurds) and Azeris (Turkicized Iranians) and some Arabs.