I was asked how it was possible that we experienced such a population explosion from 70 souls through the well over 600K men in the short number of years, even without having to factor out those who did not survive the plagues.

It occurred to me that a possible explanation might be that in promiscuous Egyptian society, particularly with handsome Jewish slave men from the non-levite tribes, that women, like Mrs. Potiphar, may have wanted relations with their Hebrew slaves, particularly with rampant homosexual relations among the Egyptian men.

This would help explain:

• matrilineal descent following Sinai - as a reaction
  
• Jewish males other than Leviim being lax in circumcision
  
• Jewish society nearly falling too low to be redeemed
  (particularly if like one explanation of why a slave might want to stay with his master, that he was happy to be a stud, that Jewish men might not have been terribly unhappy in their roles of servitude)
  
• the vast number of Jews we are told who did not survive the plagues
  
• the Jewish people being seen everywhere to Egyptian society, as a thorn
  
• perhaps one explanation for mixed multitudes
  

And perhaps a few other miscellaneous facts start to fit into place a little better.

Are there any facts counter to this theory which would need to be taken into consideration?

Rob,
Are you saying that coming out of Egypt we were fundamentally "Egyptian" and that only after Sinai did we become "Israelites"? Are you saying that before Sinai we were basically the product of Egyptian women sired by Jewish slave men?
Avi

Avi, no not at all, I am suggesting that although _we_ are the proper descendents of the Avos, that there was a loop-hole of sorts within the law such that there could be very many Egyptians among us who have a valid claim to Judaism through their father only, unlike today where that is not valid.

And of those many were raised without any connection to any Jewish parent, thus could not have had any circumcision or any Jewish identity.

We are not a democracy such that even if they did outnumber us, they do not define us, so I am definitely not saying that before Sinai _we_ were that product.

But also Egyptian men finding themselves in their households surrounded by offspring sired by their slaves could help explain the verse describing the Egyptian reaction to our population explosion.

And in this light, the change to matrilineal descent could be seen as a reaction of sorts to close off this loophole.

...

Does anyone have demographic figures for the worldwide Jewish population today in accordance with halacha, and also by a what-if scenario if we were to include in the count those non-Jews who have a non-halachic claim to only a Jewish father?

Rob,
I've heard it said that the Jewish population worldwide has never reached more than 15 million at any point in all history. It seems, as we approach this mark there is a progrom of sorts. Today we are nearing that number. Of that number there is only about 3 million frum Jews, I believe.
Avi

BTW,
I'm not even sure that matrilineal descent was an innovation. We have always had matrilineal descent although in a patriarchical society. Jewishness has always been defined through the mother, while tribal assignment and inheritence through the father. Nothing changed. Otherwise Tzipporah (wife of Moshe Rabbienu) would not have needed to convert. Based on her actions we know she converted. If Jewishness were patrilineal before Sinai, Ishmael would be a Jew too.
Avi