OK, I have heard this one too and decided to do a little bit of research on it.
I got Neal Gabler's book on Walt Disney and so I will quote it," In fact, Walt had been around Jews all his life. There were a number of Jews at the Benton School in Kansas City and even larger contigent at Mc.Kinley High School in CHicago. And though he did make some insensitiv ethnic remarks and occasional slurs, he was tolerant where it counted most and where it wasn't for public display-in his personal life." (Page 455) Also on charges of Anti-Semitism, " There is some dispute whether the same spirit of tolerance prevailed at th studio, but the Jews who worked there, it was hard to find any who thought Walt was anti-Semite. Joe Grant, who had been the head of the model department, and the storyman respinsible for Dumbo along with Dick Huemer, declared amphamtically that Walt was not an anti-Semite.'Some of the most influential people at the studio were Jewish'Grant recalled, thinking no doubt of himself, production manager Harry Tytle, and Kay Kaem who once quipped tat Disney's New York office had more Jews than the Book of Leviticus." (Page 455) There is also note of the Jewish charities he paid for.
So why the rumors? Simple, in those days Walt had a Union fight going on with the animators. The rumor is tied to Art Babbit. Also, according to the book, David Swift, also a Jew told another biogrpaher that he told Walt he was leaving another studio. Walt said something discriminatory but then again the book also says that it may have been Walt's bitterness of the strike and also it would of been uncharacteristic of him. The other theroy is because of the guilt of association. Ben Sharpseen was one of his employees and a anti-Sepmite, according to animator Art Davis.
If there is one thing Disney was against, it was communism. He joined the MPA and there was an supposed association of anti-Semitism to that. However, does that point that Disney was an anti-Semite? According to Gabler, "Walt Disney was certainly aware of the MPA's purported, ati-Semitism, but he choose to ignore it, possible feeling that the accusation was Communist propganda." (Page 458)
Now, the book "Walt Disney: Hollywood's Dark Prince" I have read and while I agree that Disney was a unflinching boss with an anger towards the communists and some union parties, I disagree with the anti-Semitism. There is not enough concrete evidence to prove that he even was. The people who had made up the rumors were disgruntled employees and the guilt of association was tied to Disney rather unfairly.