They were labeled as dhimmi. Judaism and Christianity had to be kept low-profile, and (for example) church bells, or blowing the shofar-horn, were forbidden.
They also had to pay a special tax (Jizya); and any dhimmi avoiding this payment would have his safety forfeited.

Muslims were tolerant conquerors for the time-period, but there was no concept of equal rights (especially since the concept of "rights" did not exist until the Enlightenment in Europe). Non-Muslims, called Dhimmi in Moslem-ruled state, lived in Muslim territories at the will of the sovereign.

Purely in terms of respecting the ideas of Judaism and Christianity, the Muslims were very tolerant and extolled the virtues of those faiths in addition to decrying them as corrupted. However, respect for a religion is abstract, but respect for practitioners is not.

The Dhimmi had to to the jizya, or tax for not believing in Islam. Dhimmi also had to pay additional taxes on land-holdings and these taxes where called kharaj. In addition, Dhimmi could not sell wine or pork in the public marketplace. They were not allowed to build new places of worship, restore old places of worship, or perform any act which could be viewed as proselytization. In many jurisdictions, a Dhimmi could not trust law enforcement to protect him, a judge to accept his testimony (especially against a Muslim), and in certain cases had their children stolen by Islamic rulers to be raised as Muslims (most commonly in the Ottoman Empire's devshirme system). The Dhimmi was a humiliated second-class citizen.

Muslims argue that the taxes that the Dhimmi were compelled to pay are similar to Alms or Zakat in Islam. However, Moslems pay the Zakat as an act of faith and belief in the same way that Christians paid tithes to the Church in the Middle Ages. Paying the Zakat is a privilege and an honor and a pillar of faith. Paying the jizya and the kharaj are forms of repression. The money expended by each party is irrelevant, it is the purpose behind the tax that is important.

In 1856 the Ottoman Empire issued the Hatt-i Humayun. It's purpose was to create an Ottoman national citizenship for all people in the empire. It was not entirely successful and for twenty years there were serious efforts to make the 1856 reform decree a reality.

Why and how would Jews place restrictions on non Jews???? Judaism teaches that all humans are equally G-d's children. The righteous of all faiths reaches heaven. --------------------------------------------------------------------------------------------