What were the religious effects of the initial Arab conquests in the Byzantine Empire?

Question

I've been reading some articles and books about the early Islamic conquests that started at about 634 CE, mainly in areas that belonged to the Byzantine Empire. Problem is, the majority of works I've read until now emphasize the military or administrative aspects of these events, and when religion is mentioned it is only to explain discussions and polemics about Monophysites and Chalcedonians, making it seem that Islam didn't affect the empire at all. That can't be the case because, already in 656, Syria proclaimed Mu'awiya as a Caliph, starting a civil war that would end in 661 with his victory and the creation of the Umayyad Caliphate.¹

As I am very interested in contacts between different civilizations and how they affected common people, I am curious to know if there was some kind of major conversion to Islam in the conquered provinces of Syria, Egypt, Palestine, and others in the 7th century, or if that was a slow process.

¹The Cambridge History of the Byzantine Empire, pp. 230-231

Answer 1

The Muslims did not pursue a convert-all policy in their conquered territories, one reason being that that would cause revolts and make those territories terribly difficult to manage. But this doesn't mean that there weren't any initial conversions. As Hugh Kennedy puts it in his The Great Arab Conquests:

Attraction, not coercion, was the key to the appeal of the new faith.

What he meant by this is that people were not forced to convert to Islam, and instead the situation was rigged so that it was an advantageous thing to do. Muslim people paid less taxes than non-Muslims, even if they weren't Arabs, and people could only be a part of the ruling elite by being Muslims. (Curiously, this was so even though the administrative language was still Greek for some time after the conquests.) Another key element is that it was essential to be a Muslim if one wished to pursue a military career. Of course after some time problems arose between newly-converted people and old-timers, but that goes beyond the question.

About Mu'awiya and his claim to the Caliphate in 656: his family already had properties in Syria, which let him form a power base that lifted him to the Caliphate in 661, after the First Muslim Civil War. So even though the general population didn't convert, his participation in the ruling class made him able to advance his name as a possible Caliph after the death of Uthman, the last of the Rashidun Caliphs.

All these claims are due to the aforementioned book by Hugh Kennedy.

Answer 2

Somewhat more narrowly, the traditional account of iconoclasm in Byzantium is that it was at least partly motivated by the successes of Islam with its aniconic tradition. See Byzantine Iconoclasm, with its rich caveats.