The only people it won't be popular with are the right-minded individuals who wouldn't be seen dead reading any News Corp publication. And Murdoch wouldn't give two shiny shites as to what they think about anything, let alone who he chooses to employ.
The Murdoch haters have a new bone to chew, from Murdoch's point of view, she was cleared. Even if she wasn't he would still give her the job anyway. Little or no integrity in journalism, as long as she delivers the profits then she will stay. I don't see many people who read Murdoch papers giving a hoot.