The word in Arabic for this "protected Minority" is Dhimmi, and it applied to non-Muslim "People of the Book".

Islam as a whole was largely accepting of the other "religions of Thee Book", i.e Christianity and Judaism. In exchange for paying a jizya, or special tax on the non-Muslims, they would be allowed to live out their lives and follow their own religion. Additionally, they would be exempt from paying the zakat tax that Muslims had to pay, 1/40 of your income, and from the military service Muslims would serve.

I talked about it briefly before in another post, so I'm going to copy-and-paste the relevant section:

Treatment of other Religions in the Expansion of the Empire One key aspect about the early expansion of Islam is that it did not attempt to force its way of life upon other people. Under the Caliph 'Umar, it was envisioned that Islam would be for the Arabs, who would exist as a sort of military caste above the conquered people. This meant that the conquered populations were disturbed as little as possible, and conversions were only on a voluntary basis. This precedent was set with Muhammed allowing the Jews and Christians of Arabia to keep their religion if they payed the Jizya (poll tax). This payment would make a member of the religions of the book - Jews, Christians, and later Zoroastrians - members of the protected class, or dhimmi. These people would be reserved from having to pay the aforementioned Zakat tax and from military service within the empire. This isn't to say that taxes wouldn't get absurdly high though, as Ira Lapidus notes that taxes on peasants could reach upwards of 50% of the value of thhe goods. It does however mean that the Muslim invaders were not hated. In fact, some Christian tribes had allied themselves with the Muslims against the Sassanians or Byzantines. Oddly enough, the Religions of the Book flourished in the early days of conquest with Islams coming. Many previously repressed sects were able to abound, and apocalyptic messages were numerous. This changed though as time went on. 'Umar II (r.717-720) forbade Christians to hold powerful government positions. Other successive rulers forbade minority religions to ride horses, bear weapons, or show outward religious symbols in public. Repression came in waves, as one Caliph would crack down (Such as Yazis II destroying churches and animal sculptures) and then others relent. Keep in mind through all of this that from the 7th to the 11th century, upwards of half the worlds Christians lived under Islamic rule, yet they were not forced to exile or forced to convert by force (at least in large-scale).

So it wasn't only in Iberia that this religious tolerance existed but throughout the Muslim Empires. There could be periods of stricter repression but there was few, if any, large-scale state-sponsored conversion campaigns.

Another good read on this is Dhimmi or not Dhimmi?: Religious Freedom in Early Islam by Mark Graham.

I hope that this can go a little ways towards clarifying what it meant to be part of this "protected minority" or Dhimmi!