This is all very confused. The Japanese were not further ahead than the Germans. They had a very nascent research program and had looked into centrifuges a bit but it was a very small-scale thing. The Germans by comparison had a very well-developed reactor program and had explored weapons problems a bit. I would rate the latter — the Germans had prototype reactors that they were working on — as being infinitely further ahead than the all-on-paper of the Japanese. Neither country had nuclear weapons production programs; neither were trying to make nuclear weapons, despite much confused popular history to the contrary.

The "Deutsche Physik" incident in Germany (from which the "Jewish physics" issue came from) had no specific effect on their nuclear program. By the time of the nuclear program Heisenberg had been totally successful at vanquishing the small number of physicists who believed in such things and was held in high esteem by the Nazis. One could, in a broad way, credit the Nazi expulsion of Jewish professors as one of the reasons their nuclear program was not what it might have been (this had nothing to do with the "Jewish physics" issue and was a broader Nazi program), but one gets very counterfactual indeed if one tries to imagine what a Nazi nuclear program would look like if the Nazis hadn't been Nazis.

There are people who occasionally want to believe that somehow the Japanese had some massive, totally secret nuclear program of which there is no evidence and much evidence to the contrary. Said people tend to want to believe that because they think it somehow justifies Hiroshima and Nagasaki. But it is nonsense, and bad history. The extent of the Japanese work has been very well-documented, and is not that mysterious (the US documented it extensively, and the people who were involved in it survived the war to talk about it). It was extremely small-scale.