Do Median Jews need to undergo so called ‘strict conversion’ (Hebrew: giyur lechumra) due to their limited syncretism with Islam and before that with previous incarnations of religious imperialism in the region?
There is no evidence that Median Jews ever converted to Islam and rather was the historical limited syncretism of the various eras with religious imperialism a tool for avoiding forced conversions by religious imperialism and thus rather surviving in the shadow of religious imperialism.
Since there is no historical evidence that Median Jews ever converted to Islam and new converts to Median Judaism all undergo religious conversion under the religious authority of the Northern Jurisdiction of Israel (autonomous since 930 BCE) is there no reason whatsoever to assume that Median Jews need to undergo giyur lechumra.