Did the Kharijites fight the polytheists in Islamic history, or did they fight the people of Islam and leave the people of idols, as the Prophet, peace and blessings be upon him, informed?

The Khawarij did not conquer any land or introduce Islam into it, nor did they fight the polytheists, even though they possessed power and numbers at certain stages of history. Some scholars have stated that this is a sign of prophecy. The proof for this is the saying of the Prophet, peace and blessings be upon him: "They kill the Muslims and leave the idol-worshippers. They will pass through Islam as an arrow passes through its target." This meaning was affirmed by Al-Qurtubi, Ibn Hajar, Ibn Hazm, 'Awn bin Abdullah, Al-Shatibi, and Ibn Taymiyyah.