I want to answer you in three parts, looking at national identity, religious identity, and the notion of ethnic identity.

It should be remembered that historically the Jewish people were viewed as an aberration in the societies bordering them for their monotheism, as aside from Zorastrianism (which I will touch on later), all their neighbours from the Greek invasion onwards were polytheistic. After the Roman occupation of Judea the Jews were afforded certain privileges, such as still being allowed to worship their 'one true God' without obligatory worship of the emperor as long as they paid their taxes and did not rebel against their Roman overlords. This special dispensation was carried by the Judean people as they travelled outwards across the Mediterranean as they established trade routes and merchant enterprises throughout the empire, and as such set them apart from the general Roman population. After the Judean revolt was finally quashed in 73AD, the Jewish diaspora dispersed across the empire, retaining their religious identity which hardened around the Pharisetic traditions developed after the Macabee's freed Judea from Greek influence. These traditions gave rise to the concept of identity as a form of devotion, that faith should be expressed through outward deeds, morals, and behaviours, which was especially important given that the temple in Jerusalem was unable to be used for worship (the Romans destroyed it after the revolt was crushed). This outward piety crystallised a certain identity for Jews to abide by, which in turn morphed and transformed as the Jews were persecuted under Christian and Muslim rule.

In the pre-Enlightenment European demesnes Jews were treated as outsiders, justified by the Church's view of them as Christ killers. This in turn meant that Jews were unable to get 'respectable jobs', leaving them with roles such as merchants, lawyers and bankers as avenues to make a living. This in turn concentrated wealth within Jewish families, which in turn meant that when a ruler needed money, or a scapegoat for failed policies, the Jews would be expelled (such as Edward I's edict in 1290) and their property seized. This sense of otherness meant that the Jewish community, regardless of exact ethnic origins, was viewed as 'other' and outsider by the Christian majority, and in turn meant that unlike other religious minorities (such as the Muslims in Britain prior to the British Empire) they were an easy target for scapegoating.

Richard J Evans goes into detail about how the rise of social Darwinism in the 19th Century fragmented the established order of identity politics that Europeans had prior to the Enlightenment, especially the feudal notion of birth rite and noble blood. As part of the new identity politics, colonial racialism became part of the discourse that politicians used to justify colonial practices, and the language of otherness was then applied in terms of national identity, most notoriously in terms of Jews being seen as the enemy of the state. Russia, Germany, Austro-Hungary, and France all experienced significant bouts of antisemitism in the 19th Century, where especially in Germany the notion of the Jews being seen as another race was viewed both as a scientific fact and an excuse to blame the Jews for the rise of socialism/Communism.

In light of this, it is fair to say that the notion of Jewish identity, and in turn 'ethnic' identity is very much wrapped up in the persecution the Jews received from the fall of the Roman empire to the present day.

Now, in terms of Confucianism and Shintoism, it has to be remembered that both China and Japan never saw themselves as nations bound solely to those religions to the exclusion of all others. Unlike the Judeans, who embraced the Jewish faith after their returned from the first diasphora in Babylon, China and Japan both had other religions that entwined within their national identities throughout their long and storied histories. In her translation of the Analects, Annping Chin is at pains to point out that Confuscious and his ideas had a long road to gaining acceptance within Chinese societies, with Taoism, Buddhism, and Christianity all featuring within the national psyche. The rise of neo-Confucian philosophies in the 9th Century under the Song dynasty was due to a desire to promote a purely Chinese philosophy to the populous, though at no point did the Emperors go as far as to declare the Chinese Confucian, as the nation was a patchwork of ethnicities and faiths that the Emperor could not fully mould into Han or Confucian. The same could be said of the Japanese, as both Buddhism and Christianity peculated throughout the national consciousness at various points in Japanese history.

The closest group, I would suggest, would qualify as an ethno-religious group similar to the Jews would be the Parees, who are Iranian Zoroastrians who fled Muslim persecution in Persia and settled in India. Parsi culture encourages inter-marriage within the faith, and due to their declining numbers/birth-rate have faced similar challenges to many post-Holocaust Jewish families in trying to retain their cultural/ethnic identity.

I am sure there are other more knowledgeable historians on here who can elaborate on the points I have raised, and I look forward to further discussion.

Sources: "Pliny on Essenes, Pliny on Jews"

'The Analects (Penguin Classics)' by Confuscious, translated by Annping Chin

'The Pursuit of Power: Europe 1815-1914', by Richard J Evans

The Invention of the Jewish People by Shlomo Sand

From Crisis to Community Definition: The Dynamics of Eighteenth-Century Parsi Philanthropy by David White

Edit: Thank you for the gold, first time I have received one.

Shinto is best thought of, not as one organised religion, but as a catch-all for a vast variety of various beliefs, some specific only to one small community. The idea that Shinto is one religion is relatively new and has connections to the Meiji restoration where Shinto was recreated in a way to incorporate a divine origin myth to the royal family as part of a state building mythology.[1] As far as Shinto is concerned, it only seems to be an 'ethnic' religion only because there seems to have been little effort to spread it outside of Japan. Shinto lacking anything in the way of any sort of proselytisation (if anyone has information different to that, I'd be happy to be corrected on this point).

As for Confucianism, it's also best not to think of it as a religion, but more of a philosophical school as it regards society, politics, and the general nature of the universe. This isn't to say that it doesn't have certain religious or spiritual elements but thinking of it purely as a religion might be problematic.[2] It has never been practiced by only one ethnic group and has been studied outside of China. Its origins may by Chinese but it also had a major influence in other countries, Japan again being an example. Confucianism was highly influential in Japan as it regarded many aspects of politics and law, and the samurai code of ethics was adapted from Neo-Confucianism.[3] It might also prove beneficial to keep in mind when looking at Asian religions is there is a different attitude towards faith than in Western countries. In Japan there is little if any conflict in following more than one spiritual philosophy. The attitude is, if there is something to be gained from multiple religions than that can only enhance the religious experience of the person.[4] China also has instances of religious pluralism as it concerns an individual's practices, where people can combine elements of multiple religions in a multitude of different ways (eg. Buddhist beliefs with worship or ancestors and local gods).

[1] Basil Hall Chamberlain, The Invention of a New Religion, London: Watts & Co., 1912.

[2] Mario Poceski, Chinese Religions, Routledge; 2009.

[3] W. Scott Morton & J. Kenneth Olenik, Japan: Its History and Culture 4th edition, New York: McGraw-Hill, 2005.

[4] Wilbur M. Fridell, ‘Notes on Japanese Tolerance’, Monumenta Nipponica, Vol. 27, No. 3, 1972.