The evidence of Joseph Campbell's Jew-hating comes more from casual remarks heard by people who knew him than from his published writings. For example

"In the early 1970s I worked with Joe Campbell on his Mythic Image at Princeton University Press. It was amazing to me that this man of cosmic vision could harbor such mean-spirited and seemingly unexamined biases against much of mankind. In addition to anti-Semitism, I remember in particular his vexation over blacks' being admitted to Sara Lawrence"
--Carol Wallace Orr, letter to the New York Review of Books, November 9, 1989, page. 58.

"When the astronauts landed on the moon, Joe made the repellant jest to a member of my family who was a student of his at the time, that the moon would be a good place to put the Jews"
--Brendan Gill, response to letters to the New York Review of Books, November 9, 1989, page. 60.

"At one faculty function, in 1969 or '70, I found myself drinking with Campbell and another, older, equally right-wing teacher. At some point in the evening, Campbell, responding to a remark I can't recall, said something to the effect that he could always spot a Jew. I, a Jew, said, 'Oh?' Whereupon Campbell went into a description of how the New York Athletic Club had ingeniously managed for years to keep Jews out. He went on and on, telling his story in the most charming and amiable fashion, without any self-consciousness about the views he was expressing and, indeed, without any overt animus--for all that he obviously relished the notion of keeping Jews out of anywhere any time, forever."
--Arnold Krupat, letter to the Editor, The New York Times, December 2, 1989, section 1, page 26, column 5.

This suggests a man who, like Jesse Jackson, learned Jew-hatred as a child, but, unlike Jesse Jackson, never saw the need to unlearn it.

There is evidence, though, of an even darker side of Campbell's Jew-hating mean streak. Roy Finch, a colleague of Campbell's for many years at Sarah Lawrence, in the same issue of the New York Review of Books already cited, called Campbell a "crypto-fascist". In an interview with the Boston Globe, Finch said that Campbell was a "romantic heroic fascist" (though he added that Campbell was "in no sense a bigot." I have difficult seeing how it is possible to espouse romantic-heroic fascism without bigotry, but let that go for now.) Furthermore, in an interview with Richard Bernstein of the New York Times:

"'Joe tended to lump people together,' Professor Finch said. 'So, for example, if he's criticizing Communists, he might be inclined to lump them together with Jews. He thought the left-wing, liberal, Jewish, Communist point of view was part of the degeneration that was going on in our society, and his comments were in that context.'"
--Richard Bernstein, "After Death, a Writer is Accused of Anti-Semitism", The New York Times, November 6, 1989, Section C, page 17, column 3.

Lumping "the Jews" together with the ills that are causing "the degeneration of society" is classic anti-Semitism. Professor Finch was not saying that he ever heard Campbell utter a remark of this kind, and in the Boston Globe interview he said positively that he never heard Campbell utter a racist comment. But in the statement to the New York Times, Finch is saying that he considers it consistent with what he knows of Campbell's character that Campbell would mention "the Jews" as part of "the degeneration" of society.