I've noticed a new tv PSA (that has been shown fairly frequently) about refugees fleeing to the U.S. and that notes Jesus was a refugee. I decided to research that and found this:

***Under that broad definition, it may seem that Jesus and His parents might have qualified for a time as refugees. However, there is a difference between the dictionary definition of refugee and its use as a political term today.

In the New Testament, Matthew records the following: "An angel of the Lord appeared to Joseph in a dream. ‘Get up,’ he said, ‘take the child and his mother and escape to Egypt. Stay there until I tell you, for Herod is going to search for the child to kill him.’ So he got up, took the child and his mother during the night and left for Egypt, where he stayed until the death of Herod. And so was fulfilled what the Lord had said through the prophet: ‘Out of Egypt I called my son’ " (Matthew 2:13–15).

Jesus was not a “refugee” in any sense meaningful to today’s world. For one thing, Jesus’ family never left the Roman Empire; they simply fled from one region of Roman territory to another Roman territory. That would be like someone moving legally from one state to another within the USA to leave the jurisdiction of the governor of the first state. Also, Luke makes it clear that Joseph and Mary went out of their way to follow Roman law in adhering to the census (Luke 2:1–5). Everything they did was legal.***
https://www.gotquestions.org/was-Jesus-a-refugee.html