Source? I wasn't aware that the Celtic/Italian/German population of Europe was effectively replaced by a Semitic/Greek population.
The Book was the triumph of Christianity by Rodney Stark. (I have that book along with "the case for the crusades")
His premise was that Christianity just out reproduced other religions. Some of the reasons listed.
1) Higher birth rate (the Catholic thing).
2) The fact that the Romans would often just abandon their infants on the hill side, especially culturally unwanted girls. Girls, unlike men needed numbers to reproduce.
3) Christian society tended to the sick more, which often just needed basic care to survive.
4) Missionary conversion of people was an important part of that Christian rise, but not the most important part.
5) Often a Christian female would marry a non Christian male and the descendants would be Christian.
6) The Romans were religious tolerant (Christians were willing to pay taxes to Rome) and there was less persecution than Christian mythology might lead people to believe.
7) Christianity was popular amongst the upper classes and so more culturally influential than perhaps assumed.
I get what your saying though about the impossibility of a effective replacement by a a Semitic/Greek population. Never questioned that when I read it. Perhaps small amounts of Missionary conversion was the necessary seed for expansion in a lot of places. I suspect #5,#6,#7 was a big part of it, people saying well the important people were Christian around here so I will go along even though I am not really practicing, just swept a long in the trend, vs actually getting baptized and practicing.