For other sources on the Donmeh, there's Wikipedia, the Jewish Encyclopedia, and Marc David Baer's 2009 book from Stanford University Press, The Dönme: Jewish Converts, Muslim Revolutionaries, and Secular Turks. Here's the summary by Baer, a professor of history at UC Irvine:
This book tells the story of the Dönme, the descendents of Jews who resided in the Ottoman Empire and converted to Islam along with their messiah, Rabbi Shabbatai Tzevi, in the seventeenth century. For two centuries following their conversion, the Dönme were accepted as Muslims, and by the end of the nineteenth century rose to the top of Salonikan society. The Dönme helped transform Salonika into a cosmopolitan city, promoting the newest innovation in trade and finance, urban reform, and modern education. They eventually became the driving force behind the 1908 revolution that led to the overthrow of the Ottoman sultan and the establishment of a secular republic.
To their proponents, the Dönme are enlightened secularists and Turkish nationalists who fought against the dark forces of superstition and religious obscurantism. To their opponents, they were simply crypto-Jews engaged in a plot to dissolve the Islamic empire. Both points of view assume the Dönme were anti-religious, whether couched as critique or praise.
But it is time that we take these religious people seriously on their own terms. In the Ottoman Empire, the Dönme promoted morality, ethics, spirituality, and a syncretistic religion that reflected their origins at the intersection of Jewish Kabbalah and Islamic Sufism. This is the first book to tell their story, from their origins to their near total dissolution as they became secular Turks in the mid-twentieth century.
Baer's claim of "near total dissolution as they became secular Turks in the mid-twentieth century" appears dependent upon his emphasis on Donmeh religious exercise, as opposed to, say, their continuing to in-marry, and being Foreign Minister in the last pre-Erdogan government, and so forth.