Sabbatean Judaism was founded by rabbi Sabbatai Zevi (1626-1676) who was widely recognized by the rabbinical world as the Mashiach (messiah). After he was confronted by the Grand Vizier in the name of the Ottoman sultan and threatened with death if he did not accept Islam. In response did he put on a turban so as to signal his nominal acceptance of Islam. Zevi and 300 hundred families among his Rabbinically Jewish followers were later initiated into the Bektashi order, a denomination of core Median Judaism. This was widely seen as acceptance of Islam and the rumor spread throughout the Rabbinically Jewish world that Zevi had become a Muslim. None of this was true however since he had simply made the transition from the Southern Jurisdiction of Judah to the Northern Jurisdiction of Israel.
The name “Dönmeh” (Turkish for “convert”) is a derogatory misnomer since the Sabbateans never converted to Islam as their initiation into the Bektashi order cannot be counted as conversion since they were already Jewish. Ever since the Sabbateans transitioned from the Southern Jurisdiction of Judah to the Northern Jurisdiction of Israel have Eastern Sabbateanism (the only surviving branch of Sabbateanism) been a subset of Bektashism and thus part and and parcel of Median Judaism and the Northern Jurisdiction of Israel. Even if the Sabbateans had converted to Islam does initiation into the Bektashi order count as conversion to Judaism according to Esoteric Judaism and so Zevi’s feigned conversion to Islam was null and void since he converted back to Judaism by joining the Bektashi order.
The mass initiation was hardly by chance since Zevi – the then recognized Mashiach – had no doubt been initiated by the leading poskim (rabbinic decisors) into the innermost secrets of Esoteric Judaism, including the existence of Median Judaism such as the Bektashi order. The main reason Sabbatai Zevi and the Sabbateans were excommunicated by the poskim was not that the sultan had “converted” Zevi under duress to Islam (this could easily have been reversed by Zevi fleeing to Christian lands in Europe) but rather that Zevi had risked exposing core Median Judaism as Judaism and thus also risked exposing core Median Jewry to forced conversions by political Islam by himself and hundreds of his followers transitioning from the Southern Jurisdiction of Judah to the Northern Jurisdiction of Israel. Sabbateanism is part of the Bektashi order and is thus a subdenomination of Bektashism, one of nine denominations of core Median Judaism.
Sabbatean Judaism was long centered in the Greek city of Thessaloniki until the Sabbateans living there were deported to Turkey in 1923 with the population exchange between Turkey and Greece. Due to being being Bektashis were the Sabbateans still considered “Muslims” and the Sabbateans of Thessaloniki were thus expelled from Greece just as Christians were expelled from Turkey.
The Sabbateans came to take a leading role in the emergence of the Republic of Turkey and especially through the person of Mustafa Kemal Ataturk (1881-1938), a Sabbatean born in Thessaloniki. Members of the Sabbatean community completely dominated Turkey in the 80-year period of 1923-2003 through their control of the so-called Derin Devlet (Turkish for ‘Deep State’) a domestic Turkish intelligence agency founded by Mustafa Kemal Ataturk.
The Sabbateans traditionally maintained synagogue buildings but nowadays are their synagogues mobile and highly secret in being moved between apartments. Most contemporary Sabbateans marry secular Turks and children of intermarriage are often converted to Sabbatean Judaism.
There are extinct European branches of Sabbatean Judaism including Frankism as founded by Jacob Frank (1726-1791) who claimed to be a reincarnation of Sabbatai Zevi and famously revived Sumerian ritual sex.
Hasidic Judaism first emerged as a Sabbatean sect and the influence from the Bektashi order (and Alevism) can be seen in the Tish ritual meal, joyous alcoholic consumption on other occasions than Purim and Passover and their proclivity for religious dancing. It is possible that Hasidic rebbes remain Crypto-Sabbateans who hide their true beliefs as Hasidic Jews also remain Crypto-Bektashis.