Matt 2 makes it plain the star didn't first lead to a manger but to King Herod who wanted to kill Jesus.
I know the WT says that but read it yourself. It does not say that at all. It says the Magi logically went to Jerusalem (the Capitol of Judea) after seeing a star (common sign of birth of kings) rise in the east and ask around:
“Where is the one who has been born king of the Jews? We saw his star when it rose and have come to worship him.”
The star does not move from the east to lead them to Herod, rather Herod hears about these Magi asking around and then secretly has them summoned to him.
7 Then Herod called the Magi secretly and found out from them the exact time the star had appeared. 8 He sent them to Bethlehem and said, “Go and search carefully for the child. As soon as you find him, report to me, so that I too may go and worship him.”
The star they had seen when in the east then, to their joy, reappears and helps them locate Jesus.
The twisted version of the WT is a deliberate misrepresentation of the story to demonize the familiar Xmas scene.