The jurisdiction of Israelite religion was split in two with the partition of the Israelite united monarchy into the northern kingdom of Israel and the southern kingdom of Judah in separate independent states in the year 930 BCE.
In the Middle East, the religious jurisdiction of the northern kingdom has long since been split into the six distinctive denominations of Alawite Judaism, Alevi-Bektashi Judaism, Druze Judaism, Samaritan Judaism, Yarsani Judaism and Yezidi Judaism.
Orthodox Rabbinic Judaism has been divided on the question of their recognition of the contemporary religious recognition of the northern jurisdiction of Israel as has been shown by the case of Ethiopian Jewry. Genetic testing has shown that Ethiopian Jews are not of Middle Eastern genetic origin and are rather descended from northeast African converts to Median Judaism. Ethiopian Jewry did not have access to the Talmud and were thus unaware of halakha. This means that they did not undergo halakhic conversion to Judaism and their collective conversion to Median Judaism as so many other Jewish peoples outside the Middle East in any case preceded the emergence of the Talmud by a millenium. Yet the Chief Rabbinate of Israel has recognized Ethiopian Jewry as fully Jewish although some Orthodox rabbinical authorities maintain that there is doubt (Hebrew: sofek) as to their Jewish status and therefore require that they undergo giyur lechumra (Hebrew for so callled ‘strict conversion’) so as to clarify and remove any doubts as to their Jewish status. The Chief Rabbinate recognizes that Ethiopian Jewry belongs to the Northern Jurisdiction of Israel and therefore implicitly recognizes that the Northern Jurisdiction had its own valid non-halakhic conversions.
The recognition of conversions to Judaism is a sensitive issue in the Southern Jurisdiction of Judah, i.e. Rabbinical Judaism and Karaite Judaism. The question of recognition of conversions is a major matter of dispute between the various denominations of Rabbinic Judaism.
Doubt or not, Orthodox Rabbinic Judaism recognizes that the Northern Jurisdiction at least in the past had valid non-halakhic conversions since even the “doubters” require only giyur lechumra and not full conversion for Ethiopian Jewry.
The deported Israelite tribes married freely with the Medes once the Median Kohanim had become the official priestly caste of the Median state. Present populations of Median Judaism in the Middle East have Israelite ancestry but are predominantly descended from converts. As the precedent of Ethiopian Jewry shows are their pre-halakhic ancestral conversions halakhically valid indeed.
Aside from from Ethiopian Jewry are there still remnants of converted peoples in Africa, Asia and Oceania who have remained Jewish, i.e. they have not been converted to religious imperialism, two prime examples are the the Maasai people in Kenya and Tanzania and the Qiangic peoples of Sichuan, China. There are also remaining minorities such as those Igbos of Nigeria who were never converted to Christianity and rather remained part of Odinani Judaism. Such populations of Median Jews are just as halakhically Jewish as Ethiopian Jewry and the Median Jews of the Middle East. This is despite the tragedy that most Jewish peoples are no longer Jewish as they were long since converted to religious imperialism, whether Islamic, Christian or Buddhist religious imperialism. This is true for most Igbos who became Christian, all Pashtuns who became Muslims and the Japanese who early became Buddhist. Yet the remnants of Israel remain! Am Israel Chai!