 In spite of this, they maintained ties with Sabbateans who had not converted and even with Jewish rabbis, who secretly settled disputes within the Dönmeh concerning Jewish law.As far as ritual was concerned, the Dönmeh followed both Jewish and Muslim traditions, shifting between one and the other as necessary for integration into Ottoman society.Outwardly Muslims and secretly Jewish Sabbateans, the Dönmeh observed traditional Muslim holidays like Ramadan but also kept the Jewish Sabbath, Brit milah and major holidays.