For some more background, Egypt was first conquered by the Persian Achaemenid Empire and then by Alexander. After Alexander's death it became the seat of a powerful Hellenistic kingdom ruled by the descendants of Alexander's general, Ptolemy, who reigned until Egypt was annexed by the Romans in the time of Augustus. Under the Ptolemies, Alexandria became a great center of learning and Greek and Egyptian beliefs and ideas intermixed.

During the Roman period, Egypt was one of the first regions to develop a strong Christian presence, and many of the ideas of Christian monasticism started with Egyptian monks. But these early Christian roots meant that by time the Roman Empire officially converted to Christianity under Constantine, Egypt already had its own established beliefs and practices (predecessors to the modern Coptic Church). These came into conflict with the orthodoxy set up by the Emperors and their appointed priests. Because of this religious conflict, relations between Egypt and the rest of the empire were strained. This is a factor in why there was not much pro-Roman resistance in Egypt after the Arabs took over.

By the time of the Arab conquests, Egyptian/Roman polytheism had been extirpated from Egypt by Christianity. Perhaps other users with greater expertise in Roman Egypt can discuss that process, but it was a fully completed one by the time of the Arab conquests.

The question of the Arabization and Islamization of Egypt is an interesting one. Our statistics are imperfect. Today the “official” demographics of Egypt are that it is 10% Christian and 90% Muslim. No one knows the real figures. Like many countries in the region Egypt does not conduct reliable censuses on sectarian questions. So this is an agreed upon ratio of convenience, but it “feels” approximately correct, plus or minus, say, 5%

So from the Arab conquest in the 7th century to the 21st century, Egypt went from 100% Christian to 90% Muslim. When did this happen?

The data here is also far from perfect. The basic work and method for all such estimates, at least the ones with any hint of mathematical rigor, derive from Richard Bullietts book on conversion rates. His data is better for Persia than for Egypt, but his basic estimate is that conquered territories became majority Muslim after about 200 years.

The second question is when Egypt attained the proportions that it did. Here I’m not familiar with any data-driven analyses, but have come across works claiming that it was probably in the medieval period, under the Mamluks.