It's complex but in short, the main tenets of Islam weren't a new thing in the region. Monotheism, the Abrahamic god, all those were known. And Christianity wasn't united at all, there were a lot of variations between doctrines. So it appeared as another Abrahamic faith, it was familiar. Then the Arab Muslim won militarily very quickly and brought stability to what was a war zone between Rome and Persia.

And finally, the Muslim empire were relatively tolerant of other faiths. But if you're not Muslim you have to pay a tax. So you got a faith that isn't that far from your own, their empire is successful... and if you stay Christian/Zoroastrian you have to pay... It took time but gradually populations converted on their own.

Forced conversions were pretty rare for Muslims (that's just not a thing they do as a rule, two arguments: the Quran says not to do so, and non Muslim can be a source of cash with special taxes). They integrated local populations which drifted toward Islam on their own. Again it wasn't immediate, Egypt was still mostly Christian in the 13th century (and still is 10% Christian today).

The spread of Islam saw the conquest of tribal/pastoral societies by a much more complex and organised civilisation. I found a pretty good quote on Wikipedia that holds that conversion to Islam "represented the response of a tribal, pastoral population to the need for a larger framework for political and economic integration, a more stable state, and a more imaginative and encompassing moral vision to cope with the problems of a tumultuous society."

If you can rationalise wars of conquest being relatively ‘peaceful’ paths to conversion, much more oppressive methods of subjugation and subordination - forced conversion, ethnic cleansing etc. - would come later.

From what I understand, in the early stages of the caliphate Islam was a status symbol that separated the ruling Arab elite from the masses.

Don't underestimate the efforts of Muslim traders. This is how Islam spread to most places. If you look at a map of the Muslim world, it is far wider than any of the military conquests. In fact India, where Islam had it's most successful militarism, is not considered part of the Muslim world. Regardless, the most populous Muslim nation was converted through trade and culture. So was most of West Africa. The Muslim traders even worked on the nations that became the caliphate. Trade conquered the Turks as well.

That wrong. Rome didn’t impose its polytheism. According to Roman theology the Egyptian gods were basically the same as theirs. Traditional beliefs were kept in place with some Greek influences and some syncretism. The last traces we have of traditional Egyptian religion is around the 4th century AD.

When the Muslims arrived the country was Christian. And wasn’t imposed and neither was the shift quick. It’s only in the late Middle Ages that Islam became the majority religion.