u/siantlark

This theory is not accepted, and itself has a long history going back to Saeki Yoshiro (Peter Y. Saeki), a Japanese scholar who worked in the early-to-mid 20th century, whose academic work was focused on the history of Nestorian Christianity in China. These theories build on several narrow, accepted claims, but extrapolated with no further evidence other than very biased re-interpretation of existing evidence, based on claims of similarities made out of context.

Japanese-Jewish common ancestry theory

In 1908, Peter Saeki published a book purporting that a Korean tribe that had migrated to Japan in the 3rd century was a Jewish-Nestorian tribe. This work has been heavily criticized and debunked since, but it was not nearly the first such work.

Such racialist origin theories were quite in vogue in the 19th century, in particular as a way to explain away Japan's rapid rise to modernity and industrialized society, despite being an Asian nation. As far back as the 16th century, there was speculation by Jesuit missionary João Rodriguez that the Japanese and Chinese were the Lost Tribes, even if he later criticized his own view as false.

In the 19th century, a farmer-turned-herringman-turned-historian Nicholas McLeod, a Scotsman who became a Christian missionary in Japan, published book purporting the Japanese to be descendants of the Lost Tribes, citing similarities in local legends, theologies, and racial features. Saeki Yoshiro followed the same path, and both were heavily cited by Christian missionaries even today. All that specific work on the Japanese-Jewish common ancetry has been debunked.

Repurposing some claims for Nestorianism in Japan

Now on to claims of Nestorianism in Japan in the pre-modern era. It is important to note that yes, almost surely several Nestorians had visited Japan in the pre-modern era.

Nestorians were present in China -- this isn't disputed -- and were active in the Mongol empire. Going back to the Tang era, it is likely there have been visits to Japan by Chinese Nestorians, but there is no evidence of their spread in Japan, aside from Saeki's interpretation of origins of certain names, which are considered false and are based on bad methodology. A bit later from the Yuan dynasty, we now have archeological evidence of what looks like artifacts left by Mongol soldiers in Japan which are of Christian origin. These are from the remnants of the infamous invasion of Japan thwarted by the Kamikaze winds. Once again, there is no evidence to support that this led to the spread of Christianity, if anything else these soldiers who barely made it to Japan were likely to have been persecuted. Saeki goes on to claim that because in his interpretation certain symbols of Buddhism had Christian origins, then it must be that there was lasting influence of Christianity.

Following WW2, Ikeda Sakae wrote in the 1949 issue of Light from the East, a Nestorian periodical, claiming the presence of chapels and churches in Kyoto with Nestorian origins, basically citing Saeki's old (debunked) work again. Later on, in the same publication, Ikeda makes an original claim that a likeness of a Nestorian missionary Mar Toma, who supposedly came to Japan and died in 601 CE, is venerated in a temple near Kyoto. The problem is, other than Ikeda's interpretation of a Buddhist shrine, there is not other evidence supporting the claims.

To make all the above even more complicated, Ikeda tends to publish his claims in Light from the East, a decidedly non-academic forum and one who doesn't claim to be anything more than a forum for Nestorians, occasionally but not always linking back to Sakae's work. Further, these are written in the same articles in which he communicates with Nestorian church leaders encouraging them to "re-establish the Nestorian church in Japan." All of this is very tiring to sift through. Therefore, in academic history, these theories are not taken seriously and are rarely discussed. To be honest, it's tiresome to debunk such theories because in the end one to focus the claimant's methodology, itself not a very productive exercise in advancing academic history.

TL;DR This is the latest of several theories that have been debunked. The method of looking at Buddhist temples and symbols and re-interpreting them as having Christian symbols, out of context, is very bad history.

The best summary of this are in Gilman and Klimkeit's Christians in Asia Before 1500, Routledge 2016; and more critically in J. H. Morris's The Presence of Jingjiao in Japan as explored by Ikeda Sakae, Japan Missionary Journal, 2015.