The hot takes on Jesus and the border wall on Christmas are cheap, if not idiotic. They were in Bethlehem to be taxed, not as refugees.
I understand your point, but that’s due to poor framing by ill-informed tweeters looking to make a quick point.
Mary and Joseph’s time as refugees was their stay in Egypt, after fleeing Herod’s slaughter of the Bethlehem infants (Matthew 2:13-23)
Their flight and exile to a foreign, suspicious land fits them into that category. Compared to that, their time in Bethlehem was a tax-induced road trip with poor accommodation.