Early rabbis of the Talmud (Rabbis Akiva, Eliezer and Shimon) who commented on the whereabouts of the descendants of the ten tribes identified them as collective sinners, meaning heretics but clearly recognized them as Jewish. The rabbis disagreed among themselves as to whether God would allow the descendants of the ten tribes to return to the land of Iand of Israel in consideration of their collective “sins”, meaning their syncretism with religious imperialism, yet they were nevertheless recognized as fully Jewish. However already at that time were most Median Jews long since descended from ancient converts to Median Judaism and that apparently was not a problem to the esteemed rabbis just as the chief rabbis of Israel recognized the pre-halakhic conversions which the ancestors of Ethiopian Median Jews underwent in ancient times.
When rabbi Sabbatai Zevi chose initiation into the Bektashi order over forcible conversion into Islam did he know perfectly well what he was doing as he no doubt as the then recognized Mashiach had been initiated into the secrets of Esoteric Judaism by the top poskim (rabbinic decisors) of his generation including knowledge of the existence of denominations of core Median Judaism (such as the Bektashi order) which have always remain recognized as halakhically Jewish for the simple reason due to remaining endogamous and remaining Jewish. Their tactical syncretism with the religious imperialism of the era was always considered heretical but they were no less Jewish.
What then about their conversions? Since the rabbis recognize these seven denominations (Alawism, Alevism, Alianism, Bektashism, Druzism, Yarsanism and Yezidism) as legitimate is there no reason not to recognize their conversions and to invalidate their conversions would be to invalidate the halakhic stature of their entire communities since they are predominantly descended from ancient converts and only minimally from Israelites who were most likely a small population at the time of the Assyrian deportations or it would had been logistically difficult to deport them from ancient Israel.
Will Orthodox rabbis cease to recognize conversions of core Median Judaism once mass Aliyah (immigration to Israel) of Median Jewry commences, in order to maintain its Jewish monopoly on conversions in Israel? Only time will tell.