In the Levant, Lebanon remained a majority Christian region until less than a century ago, and Upper Egypt is still majority Christian. In both places emigration and slaughter by Muslims, rather than conversion, has been the main cause of demographic change.
Evidence shows that the Egyptian population is homogeneous
Genetic testing shows that the Egyptian population is quite mixed, maternal markers showing contributions from the horn of Africa (especially close to the Tigre) and paternal ones showing links to Saharan populations. The high level of cousin marriages etc. (among both Copts and Muslims) does have the effect of homogenizing the population (as inevitable some do not marry their cousins).
The geographic location of Egypt, at the interface between North Africa, the Middle East, and southern Europe, prompted us to investigate the genetic diversity of this population and its relationship with neighboring populations. To assess the extent to which the modern Egyptian population reflects this intermediate geographic position, ten Unique Event Polymorphisms (UEPs), mapping to the nonrecombining portion of the Y chromosome, have been typed in 164 Y chromosomes from three North African populations. The analysis of these binary markers, which define 11 Y-chromosome lineages, were used to determine the haplogroup frequencies in Egyptians, Moroccan Arabs, and Moroccan Berbers and thereby define the Y-chromosome background in these regions. Pairwise comparisons with a set of 15 different populations from neighboring European, North African, and Middle Eastern populations and geographic analysis showed the absence of any significant genetic barrier in the eastern part of the Mediterranean area, suggesting that genetic variation and gene flow in this area follow the "isolation-by-distance" model. These results are in sharp contrast with the observation of a strong north-south genetic barrier in the western Mediterranean basin, defined by the Gibraltar Strait. Thus, the Y-chromosome gene pool in the modern Egyptian population reflects a mixture of European, Middle Eastern, and African characteristics, highlighting the importance of ancient and recent migration waves, followed by gene flow, in the region.http://muse.jhu.edu/login?uri=/journals/human_biology/v074/74.5manni.html
Myself, I've seen a blond Copt fellahin who could have passed for a Swede (I know: I"ve part Swede and I've been to Sweden), down in the deep rural parts of Upper Egypt (near Deir-alMuharrak, where St. Joseph got the dream to return to Palestine). In Aswan I met a Nubian with deep black skin and blue eyes (back in the days before color contact lens. He was quite insistent about how he was Nubian, not Egyptian). And I've seen every gradiation in between amongst the Egyptians. (I've seen quite a range in the Turkish Republic too, btw).
It would take a lot to change the gene pool of 80 million, but we haven't always been that many. At the time of our last invasion (the British, 1882) the population of Egypt was 7 million, having hovered around 4-5 million for millenia. The problem is that we have been getting immigrants from so many sources for so long from the same places, that genetic studies may only indicate the continued influx (which continues: the wives of the present (and so the mother of the future) and past presidents have British roots. This has been going on since the the 3rd millennia BC, when a writer complains that foreignors come into the Valley and "become people" i.e. Egyptians. The word for Syrian/Hittite became the word for "slave" (their source), and "Mede" became the word for soldier (after the Persian invasion: we had Libyans/Berbers, and Nubians too). When Alexander came, he promoted his policy of importing Greeks (already under way for centuries in Egypt) and intermarrying. The conversion to Christianity only accelerated that, with the Egyptians adopting the Greek alphabet over their hieroglyphics to write their Egypitian language, now called Coptic, which didn't fully die out until the 17th century.
and the Islamic conquest didn't bring any noticeable contribution to the Egyptian genetic pool.
The invasion which we are interested in, of course, is the Arab one under 'Umar. Literary, linquistic and archeological evidence shows that the Muslim Arabs kept to themselves in the Amsar (millitary settlements) in Fustat and outside Alexandria, whereas the bulk of the rest of the country remained Coptic. Many of the Chalcedonian population (mostly Greeks and others, but including Copts) left for the Roman Empire. Things didn't change much until the Fatimids came with their Berber troops, and then imported Turks, Kurds and Arab Bedouin (the later which they sent to your neck of the woods) troops. Being the conquerors, they had the lion share of resources (food, women, etc.). They also brought in a lot of slaves, who were Islamicized in the process. The destruction of the Coptic majority didn't happen until al-Hakim (who had a Greek mother) instituted consistent and prolonged persecusion, a rarity in Fatimid Egypt. Something which can't be said of the Mamluks, who raped the country in more ways than one and left us in the state Napolean and the Modern World found us in his invasion.
So in Lower Egypt we had the constant influx of new, Muslim rulers, to which the Copts of Lower Egypt responded mostly by fleeing south to Upper Egypt.
Btw, another issue of demography is the large monastic population of the Copts (St. Anthony after all organized monasticism in Egypt) versus the troops the succession of Muslim lords brought in, who tended to keep the whore houses going (there are a number of interesting records from the Mamluk period on the protistution trade and the army), along with all the slaves (the biographies of Muslim personalities in a huge proportion have a slave mother) and were fruitful and multiplied in the main centers of power, while the Copts retreated to the desert and the countryside.
The last major Muslim invasion was Muhammad Ali, who brought in lots of Albanians, more Turks, Armenians (not the first time: they came during Fatimid times. They do not, however, intermarry much so do not contribute to Egypt's common gene pool) and Greeks.
My son's godmother is a Copt who is part Arab (from Lebanon) and Greek (from Greece), besides Copt.
I'm Moroccan, and like you, I know that you can spot an Egyptian from a crow of thousand as I can spot a Moroccan or Algerian brethren of mine. they have very distinctive facial features which are the same among both Christians and Muslims.
Meriam George, a Copt (and hence hard core Egyptian), and Miss Earth finalist.
Considering that and considering that the Egyptian population is verging on a disastrous number of 80 million human, you claim leave us with three choices.
As Egypt only had about 4-5 million two hundred years ago, and this has increased 1700%+ over that time this
1) Muslims indeed slaughter the Christians but left a few couples and forced them to procreate like rabbits and provided them with some futuristic medical technology to ensure a high rate of child survival, and then they Islamized those children and from them the nearly 70 million Muslim Egyptian were born.
is just plain ridiculous and uncalled for. A small population has mushroomed, not matter how you look at the data. As I said, Upper Egypt has remained the haven of the Copts, until the rise of the recent Islamists there. Whereas the Muslims had a constant influx of numbers, and Copts numbers were kept down by themselves (monasticism) and their rulers (persecusion), both amply documented.
2) You're misinformed.
3) You're just making stuff up.
I see no reason to start. I'll stick with the facts.
Since the first choice is physically impossible
The demographic history says otherwise.
and since you're a Christian
I'm not Copt. My people came in from Syria with Muhamma Ali.
which means the third is also impossible, we are left with the second choice.
Come up with some documentation that supports your contention.