Translation of Luke 2:2

[theophilus]

Anyone know anything more about this apology?

This article contains a possible explanation:

http://www.biblehistory.net/Quirinius.pdf

Here is one paragraph from it:

And as for Quirinius being the governor of Syria during this census, it is worth noting that the Bible never calls him the governor, at least the New King James Version doesn't. It says he was governing in Syria. And we know that Quirinius was indeed governing in some capacity in this region at
this time.

"Luke" and "Matthew" (names made up by later editors) were telling stories to different audiences. With the focus on Jewish rites, customs and personalities it would appear that whoever wrote "Matthew" was writing for a Palestinian audience, whereas the author of "Luke", with his focus on Roman personalities was writing for a Greco-Roman audience that didn't give a shit about Jewish rituals.

You are probably right about their writing for different audiences. The book of Acts ends with Paul living in Rome so it was probably written at this time. Since Acts is a continuation of Luke's gospel they were both probably written at the same time and were addressed to the Roman Christians, who were mostly gentiles.