The Iraqi kurds would have been pulverised by Saddam in 1990s, or by ISIL, had there not been the support from Iran.
Kurd politians and militant groups are far from innocent angels.
Iraqi Kurds are not the same as Syrian Kurds. Fact.
In Iraq 98% is said to be Muslim, 75% Sunni 25% Shia. I suspect many of both are secular in view. Both were helped by the US military. (some lapses in that) They are largely Tribal in nature.
In Syria from my information, it is more a mixture, depending upon where you are located. Significant portions of Christian and atheist. Also with Armenian, Assyrian, Alevi and Ezidi components in the areas they inhabit. The mixture clearly gets along better in Syria than in Iraq.