There were, obviously, several factors. Not the least of these were the sense of faith and tradition felt by individual believers.

More broadly, the rulers of Muslim Spain were not overly concerned with converting the population. They were no doubt influenced in this by the Prophet’s exhortation in the Quran that, “there shall be no compulsion in religion” (2:256). And again, “Truly those who believe, and the Jews, and the Christians, and the Sabaeans – whoever believes in God and the Last Day and performs virtuous deeds – surely their reward is with their Sustainer, and no fear shall come upon them, neither shall they grieve” (2:62).

More cynically, the rulers had a financial interest in preserving non-Muslim citizens, since they could be taxed at a higher rate. This combined with a real appreciation for the Quranic principles described above, led Muslim rulers such as Abd al Rahman I to be some of the most enlightened rulers of the age. Google the great Mosque of Cordoba, a beautiful monument to the success of cosmopolitan, Muslim Spain. Another legacy of the period is the eventual influx, largely via Arabic translations made in Spain, of Greek learning—not to mention the brilliant work of the philosopher Averroes, who was born in Cordoba.

So, to answer your question, native tradition and faith merged with a caste of rulers more interested in preserving diversity than destroying it.

Source: God’s Crucible: Islam and the Making of Europe by David Lewis