Craster's bloodline is special because the Others accepted his boys.  He has a good relationship with the Others because he gives them his boys.  A lot of wildlings would glady do that.  There would be no need for the wildlings to flee from the white walkers if they can keep the Others happy with the gift of an occasional baby boy.  So the baby's DNA is clearly important.  The Others do not want just any baby.  It has to be a boy and it has to come from Craster.  The Night's King was a Star