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I think that's a whole of conjecture and mistaking what are most likely unrelated similarities in culture for causal relationships. It's like saying that the ancient Egyptians traversed the globe because pyramids can be found all over the world.
The ancient Jews most certainly traveled and interacted with foreign societies. And they did form colonies in areas (such as the Kaifeng Jews of China). The similarities found in Middle Eastern groups is to be expected; the forerunners of these groups formed in the same region as the ancient Jews and would have had similar customs. Add in the history of the periods of the Jewish exile and their integration and assimilation into the dominate groups, and you're going to have a lot of hits.
It's always possible that some Jewish traders or merchants made it to Japan in the early common era, but I don't know of any scholarship that indicates it would have been in numbers great enough to have any impact on Japanese society.