Let us recall that Luke 2:1-5 connects the time of Jesus' birth (usually dated before Herod's demise in 4 BCE) with the census carried out by Quirinius, which took place in 6 CE. This Lukan anachronism has been troubling. According to some scholars, however, the link of Jesus' birth with the census might be intentional, perhaps even the product of a Christian Zealot group that connected the birth of Jesus with the rise of their own patriotic movement, led by Judas the Galilean; see Braunert, "Provinzialzensus" 212-14. It should not be ruled out that the link was aimed at conveying the memory of a relationship of Jesus and his group with the Fourth Philosophy.
(Bermejo-Rubio, They suffered under Pontius Pilate, note 195, page 195, my bold)
I have found this article by Braunert available here:
https://www.jstor.org/stable/4434523
What does it say?