This is a very difficult one. I believe what Pastor Windle proposes is that Quirinius was a Legate of Syria who conducted the registration in service to Herod the Great--who was the central authority figure of Judea at the time.
Brian needs to study more, Luke is saying Mary was pregnant in 6 CE and if that was the case, Matthew is contradicting Luke when he says Jesus was born during Herod the King's lifetime. The general consensus is Herod died in 4 BCE
If the Romans levied poll taxes, taxes levied on individual persons, then any census that counts people would ultimately be a registration of people so the tax authorities would know how much tax revenue they can expect.
Reality check: Herod the Great died ten years before Quirinius took authority as governor of Syria. Nazareth, where Joseph and Mary allegedly lived, was not under the authority of Quirinius. Every census undertaken by Raman authorities, all 323 of them, counted people where they lived on the date of the census - just like the US census today. In all of history, in all of the world, there is no evidence that any census, anywhere, was ever conducted that required people to travel to some ancestral home. Not one. Not ever. The census that Quirinius undertook in 6 CE was to levy tax on the population, because the Romans had taken authority from Herod's son, who ascended on his father's death. This census, like every Roman census, counted men where they were living. The entire birth story of jesus, this one of the two different stories in the bible, is patently and utterly false. It cannot be harmonized with known, well-proven historical fact. It is simply a lie.