The first response is the most accurate:
Muslims and Jews worked together in the economy, but lived by different laws passed by the Muslim empire.
During the Middle Ages in the Middle East, Jews and Muslims often interacted in commercial endeavors and shared many aspects of cultural and intellectual life, particularly in cities where they lived in close proximity. However, Muslims were governed by Islamic law (Sharia), while Jews followed their own religious laws, such as Halakha, leading to a complex relationship where they could cooperate economically while still maintaining distinct legal and religious identities.