Median Jews in the Middle East currently lead precarious and often oppressed lives. In Iran are all Median Jews with the exception of the Zoroastrians denied basic freedom of religion. Article 13 of the Iranian constitution recognizes Christianity, Islam, Judaism and Zoroastrianism but no other forms of religion. Alevism, Bektashism, Mandaeism, Yarsanism and Yezidism, all forms of Crypto-Judaism are completely criminalized in Iran with heavy penalties for practitioners who get caught. Rabbinic Jews in contrast are oppressed by the regime but are still a recognized religious minority with religious rights. If these severely oppressed denominations were officially recognized as Jewish by the regime would they gain freedom of religion and their situation would drastically improve. Official Israeli recognition of these denominations as Jews would therefore not harm those communities and most Iranians today are generally pro-Jewish and pro-Israeli so such official Israeli recognition would favorably influence the views most Iranians hold of those communities.
In Turkey do rabbinic Jews generally lead far more secure lives than in many European countries. Alevis (who make up the vast majority of Median Jews in Turkey) are in contrast oppressed and reviled in Turkey and Alevis who live with Muslims in the cities are typically in the closet about being Alevis. Rabbinic Jews are generally a high status group in Turkey which is much admired in the country despite the existence of pervasive Anti-Semitism in society. Once Israel officially recognizes Alevis and other Median Jews as Jews will that likely have a very positive effect on the social status of Alevis and other Median Jews in society although it will of course also expose Alevis and other Median Jews to Anti-Semitism and potentially severely so.
In Iraq is the situation different and official Israeli recognition of Median Jews is likely to have a very negative impact on the situation of those Median Jews living in Arab society while it will positively impact those living in Kurdish society which is the vast majority.
In Syria is the situation similar to that of Arab Iraq and many Muslim Arabs are likely to react negatively to Median Jews when they are officially recognized as Jews by the Israeli government.
In Lebanon is there also likely to be a negative impact although less so than in Syria.
Anti-Semitism is pervasive in Arab societies and so will official Israeli recognition no doubt negatively impact those Median Jews living as minorities in the midst of Arab Muslim society such as e.g. Palestinian Bektashis.
Although there will be some negative impact will official Israeli recognition of core Median Jewry as Jews generally overall have benevolent, favorable and positive consequences.