“If they can’t get that right, then what else don’t they know?”
“...they followed the ‘star’ to Christ’s birthplace in a stable in Bethlehem, as described in the Bible.”
To answer your question, here’s one other thing they don’t know - the Bible never says they went to the stable...
Didn’t the wise men also find Christ as a “small child” and not an infant? This would suggest that they arrived a significant time after the birth. Thus the two dates may not be incompatible.