There is no conflict on that in the bible. Both nativity accounts in Matthew and Luke place his birth in Bethlehem as Joseph and Mary are on the road to the census. They were leaving from their hometown of Nazareth to which they returned and raised Jesus after his birth. Jesus is called Jesus of Nazareth because people were called by their hometown not where they were technically born

There is no conflict on that in the bible. Both nativity accounts in Matthew and Luke place his birth in Bethlehem as Joseph and Mary are on the toad to the census. They were leaving from their hometown of Nazareth to which they returned and raised Jesus after his birth. Jesus is called Jesus of Nazareth because people were called by their hometown not where they were technically born