It is true that there were two different Bethlehems in ancient Israel. The smaller of the two, Bethlehem Ephrathah is the one referred to in Micah 5:2. It is the one in Judea. It also just so happens to be the ancestral home of David and the place where Jesus was born. That there are two Bethlehems, and that both David and Jesus were born in the same one is stronger evidence for the inspiration of the Bible, not weaker evidence as the critics claim!!! Skeptics of the Bible are pointing out information which creates an even stronger argument for the Bible and for Jesus being Messiah. It is strange that they try to use this evidence, because the clear indication is even stronger for the prophecy having been fulfilled by Jesus. Are they saying that Jesus was born in the wrong Bethlehem? If so, they are just plain wrong, as all Christians know which Bethlehem Jesus was born in. He was born in the one quite close to Jerusalem. He was born in Bethlehem Ephrathah.
Having said that, the other argument being put forward by these folks is that the New Testament writers simply invented the idea that Jesus was born in Bethlehem Ephrathah. Again, this seems to me to be a very unlikely scenario for more than one reason. First of all, true believers in Christ believe in him because they believe the evidence about him is true. If you believe it is true, then you would not deliberately (The key word here is deliberately) create a falsehood to support a thing that you actually believe is true based on reliable facts, such as Jesus’ crucifixion in Jerusalem and his tomb having been empty. Besides, when the gospels were written, there were some still alive who could remember the slaughter of innocent children by Herod, which occurred in the area around Bethlehem Ephrathah. This was not invented, and there were contemporaries who were aware of what Herod had done. The magi did not go to the other Bethlehem! This, too, supports the idea that Jesus was born in Bethlehem. If these skeptics are right, then some very important Christians, who lived otherwise impeccable lives, are flat-out lying. James, the brother of Jesus, who would know, believed that Jesus was born in Bethlehem Ephrathah. He was killed after the gospel of Matthew was written. Could he have been deceived about where his own brother was born? I do not think so. This is not a reasonable proposal.