The views of the rabbis of the Talmud on the descendants of the Ten Tribes strongly suggest that the senior poskim (the most important rabbinic decisors) of each generation have always been aware of the existence of core Median Jewry and core Median Judaism. This is strongly reinforced by the fact that rabbi Sabbatai Zevi (who had obviously been introduced into the secrets of Esoteric Judaism by senior poskim of his generation) not coincidentally and rather revealingly opted to become a dervish in the Bektashi order, one of nine denominations of core Median Judaism.
There have always been conversions to Judaism. When the fleeing Atenist priests (the ancestors of the Levites) arrived in Canaan from Egypt they apparently began converting the local population to Atenism although they continued to in parallel practice Canaanite religion for many generations. The population of the Northern Kingdom of Israel was deported by the Assyrians to what is now Kurdistan in the 8th century BCE. The descendants of the deported Israelites converted the Medes to Israelite religion in the 7th century BCE. Also the Southern Jurisdiction of Judah performed conversions long before the emergence of the rabbis and the Talmud.
How then do the senior poskim view conversions to Median Judaism? They obviously recognize pre-rabbinic conversions and there is every indication that they recognize the validity of the Northern Jurisdiction of Israel and by implication its pre-rabbinic conversions. What then about Median Jewish conversions in the rabbinic era? There is absolutely no reason to believe that rabbinic recognition of Median Judaism ever ceased considering the rabbinic redemptive hope that Median Jewry will at some point return to the land of Israel. On the contrary, if the senior poskim had deemed Median Jews non-Jewish then surely obviously they would have written off the descendants of the ten tribes as the hope of the return of the descendants of the ten tribes instead was always kept alive. Thus we can conclude that the senior poskim continue to recognize Median Jewish conversion practices such as initiations into the Bektashi order as perfectly valid conversions to Judaism.