One of my sunni friend told me that "Khalid ibn al-Walid was sent by Prophet Muhammad(SAWW) to destroy the image of the Goddess al-Uzza which was worshipped by polytheists; he did this successfully."
What is the authenticity of this statement and does it imply on muslims that under Islamic rule, we are obligated to destroy the idols of other faith?

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Yes historical reports indicate that the Prophet (s) sent Khaled to do that. However, Khaled committed a big mistake there, and the Imam Ali (a) was sent to fix it up.

Under Islamic rule, if idol worshippers are living in close proximity to Muslims and they don’t have a treaty with Muslims, then yes Muslims can destroy their idols. But if they have a peace treaty with Muslims, then no. Muslims must abide by the peace treaty. The tribe Khaled was sent to did not have a peace treaty with Muslims.