No. Actually it is people like you who are trying to distort Bible truth. First of all, it was not the decision of Joseph and Mary that led to their going to Egypt. That was A DIRECTIVE FROM GOD. So they were not mere "refugees". They were directed by God to go away for a short time.Baloney. No one was talking about their return to Judea, but the fleeing from it (as a refugee). They hid out in Egypt until Herod died sometime around 1BC as scholars reckon. Don't Americanize their story to suit your political biases.
And when they were departed, behold, the angel of the Lord appeareth to Joseph in a dream, saying, Arise, and take the young child and his mother, and flee into Egypt, and be thou there until I bring thee word: for Herod will seek the young child to destroy him. (Mt 2:13)