The first form of Judaism was ancient Sumerian religion as the Torah is comprehensively based on Mesopotamian stories, i.e. ancient Sumerian narratives. The first split in jurisdiction in Judaism is therefore between Mandaean Crypto-Sumerianism and Jewish Crypto-Sumerian Atenism. The second split in jurisdiction in Judaism occurred with the partition of the United Monarchy of Israel into the Northern Kingdom of Israel and the Southern Kingdom of Judah in 930 BCE. The Assyrian deportations in 745-715 BCE of the Israelite population of the Northern Kingdom of Israel brought those Jews to what is now Kurdistan and they later spread throughout ancient Media and the Median Empire where Median Judaism syncretically became the official religion when the Median Kohanim became the official priestly caste.
For 27 centuries have there been a de jure halakhic religious division of religious halakhic authority between the Southern Jurisdiction of Judah and the Northern Jurisdiction of Israel, including importantly as involving conversions. This is not to mention the millennia of divided religious jurisdiction between Mandaeism and Judaism. Later divisions of jurisdictions inside the Southern Jurisdiction of Judah are the 8th century CE emergence of Karaite Judaism and the emergence of non-Orthodox movements in Rabbinical Judaism in the 19th and 20th centuries CE. The Northern Jurisdiction of Israel (i.e. Median Judaism) has however since millennia split into numerous distinct jurisdictions in the Middle East and worldwide.
Ancient conversions to Median Judaism predate the rabbinic invention of halakhic conversions (and indeed predate the rabbis themselves!) and are indisputably halakhically Jewish although some Orthodox rabbis still demand that Ethiopian Jews undergo giyur lechumra, so called “strict conversion” to remove all “doubt” (Hebrew: sofek) about their origins. No one however demands that Ethiopian Jews undergo full conversion for non-Jews.
The point here is that Orthodox Rabbinical Judaism recognizes the religious authority of the Northern Jurisdiction of Israel as parallel to its own. For this reason are not only ancient conversions to Median Judaism halakhically valid due to the halakhic split of religious authority between the Southern Jurisdiction of Judah and the Northern Jurisdiction of Israel but so are also later conversions performed by denominations of the Northern Jurisdiction of Israel (i.e. Median Judaism), including by Bektashism in Turkey and Albania. This is true in halakhic terms and certainly in terms of the Law of the Return.