Because there were two towns with the name Bethlehem, almost every reference
to the southern Bethlehem either mention that it is in the territory of
Ephrata (Tanakh) which later became part of Judea, so “of Judea” (both
Tanakh and New Testament). This specificity in both Tanakh and New Testament
rules out that Bethlehem of Galilee could be meant.
Whether you believe it or not is not the issue, and not a point to argue,
all I mention are the linguistic clues.