Wolff, who spent lots of time with Murdoch for an authorized biography, has the explosive background (emphasis mine):
Gary Ginsberg, his long-time aide - part chief-of-staff; part PR consigliere - was often hurt and confounded by Murdoch’s jibes, insensitivities, and humor (there was the Christmas every executive desk got a crèche by order of the boss). Once, with me, Murdoch got into a riff about Jewish groups and money: how they were good at tricking him out of his dough.
And yet, as soon as he focused his business attentions on the US and New York in the mid-seventies, he started to hire Jews as his closest advisers. His support for Israel has been absolute. Arguably, it is his support for Israel, and for neoconism in general (for many years, he owned and funded the losses of the Weekly Standard), that helped solidify rightwing support for Israel. (I was once at an Anti-Defamation League dinner where Rupert Murdoch presented Silvio Berlusconi an award for meritorious conduct with respect to the Jews.)
I think that Murdoch, a man not so much paranoid as he is realistic about his enemies, is parsing what he sees as “‘good Jews” from “bad Jews”. Jews are just another subset of the people who are for him or against him, who he either has to manage or isolate. Along with his open dislike of Muslims - once, he explained to me his theory about how Muslims often married close cousins, therefore depressing their general IQ - and his geopolitical views about world domination, supporting Israel, I believe, is a way to win the support of what he perceives as the good Jews. (That is, if you support him, you are a good Jew.)