Why would arabs think that kurds are christians?
If anything, they are sunnies just like the rest of them, just with a different ethnic background.
And Islam, requires them to support fellow muslims, regardless of ethnicity (Mohammad may have crazy, illiterate, and a pedophile, but he also knew you got to make sure you unite your army somehow).
Off topic. I seem to notice that Arab Muslims don't help non-Arab Muslims. I remember when the Indian Ocean tsunami happened, Arab Muslims did not help their fellow Muslims in Southeast Asia, especially from the Gulf states. Yes, I know they are Polynesians. Saddam Hussein invaded Iran, which is ruled by Persian Shiites, to show the Arab world they can take Iran's land. That's why Arabs of all religious faith sided with Iraq. Saddam had non-Muslim Arabs in his government like Tariq Aziz (Michael Yuhanna).