I think this website on the subject helps one see the tweaking nature of stories passed on about gods and men.
Luke 2:1-6
In those days a decree went out from Caesar Augustus that all the world should be enrolled. This was the first enrollment, when Quirinius was governor of Syria. And all went to be enrolled, each to his own city. And Joseph also went up from Galilee, from the city of Nazareth, to Judea, to the city of David, which is called Bethlehem, because he was of the house and lineage of David . . .
P. Sculpinius Quirinius was legate (governor) of Syria in the years 6 - 7 AD. He did order a census. However, the assumption that Jesus was born in the year of Quirinius's census (6 AD) leads to irreconcilable chronological problems in the subsequent events of his life. It is entirely unlikely that Jesus was born in the year of Quirinius's census; most scholars put Jesus' birth around 4 BC, a good ten years before Quirinius's census.
The remainder of Luke's account is also highly improbable (I'm being generous here), for a number of reasons:
- There was no census of "all the world" (read: the entire Roman Empire) declared by Augustus; at least, if there were, it's not mentioned in any Roman documents that we've uncovered so far. The census was of Judea, Samaria, and Idumaea--not Galilee (where Luke puts Joseph and Mary). Quirinius used the opportunity to also conduct a census of Syria.
- The notion that each male would have to register in the home town of a remote ancestor is unbelievable. The entire Roman world would have been turned upside-down. There would surely have been records of such widespread dislocations, and there are none. Augustus was arguably the most rational of the emperors, and would never have ordered such an irrational thing.
- Ancient census-takers wanted landowners to be connected to their land, for tax purposes. The census-takers traveled, not those being taxed.
So, almost all scholars agree that it is not reasonable to think that there was ever a decree that required people to travel for purposes of tax registration.
Why, then, do we have Luke's account? Luke wanted to report that Jesus was born in Bethlehem, the City of David, in order to fulfill various prophetic interpretations. On the other hand, he also wanted to report that Jesus grew up in Nazareth, presumably for historic reasons. He thus reported the story of Joseph going to Bethlehem where Jesus was born, and then returning to Nazareth where Jesus was raised.
Matthew does something similar, but has Joseph and Mary living in Bethlehem, then fleeing to Egypt until Herod died, then returning to Bethlehem, finding another Herod in place, and so moving to Nazareth (where there was actually a third Herod, namely Herod Antipas. One of the difficulties of describing any of this is that the whole damn family was named Herod.)
So Luke reported that Jesus was born in Bethlehem but raised in Nazareth. Why report a census? Well, there were riots after Herod's death in 4 BC and again at the time of the census in 6 AD, so it is possible that Luke (or his source) accidentally combined the two riots and the two dates. A ten year error is relatively slight for ancient authors, working without archives, without a standard calendar, and writing about a period around 80 years earlier.