Ethiopian Jewry are descendants from ancient converts to Median Judaism. The Orthodox Chief Rabbinate of Israel explicitly recognizes Ethiopian Jews as coming from the Northern Jurisdiction of Israel and obviously realizing that they are descended from ancient converts, considering that they genetically are not descended from Israelites. This is an important acknowledgement by Orthodox Rabbinic Judaism that Median Judaism has autonomy in the matter of conversion and is entitled to perform its own valid conversions. There has in fact been a de jure religious division of jurisdiction since 930 BCE when the United Monarchy of Israel split into the Northern Kingdom of Israel and the Southern Kingdom of Judah. Rabbinic Judaism of the Southern Jurisdiction of Judah has always acknowledged the legitimacy of the Northern Jurisdiction of Israel, i.e. Median Judaism.
But aside from halakhic legitimacy, there is also the right to immigrate to Israel under Israel’s Law of Return. Some members of denominations of core Median Judaism on occasion pass off as Muslims despite not being so. Some denominations of core Median Median Judaism have a superficial Islamic veneer (e.g. references to Islamic names in liturgy) despite not being Muslim and never having converted to Islam. This was done in order to avoid to being forced to convert to Islam and to fit into Muslim civilization.
Israel’s Law of Return is clear, any Jews, their children, grandchildren and spouses are entitled to immigrate to Israel. This includes converts to Judaism of any established Jewish denomination. Israel’s supreme court has ruled that those Jews who converted to other religions as well as their descendants have forfeited their right to immigrate to Israel under Israel’s Law of Return and Israel’s Chief Rabbinate requires that they undergo a so called ‘strict conversion’ (Hebrew: giyur lechumra) to return to Judaism in order to regain their right to immigrate to Israel.
Does this include denominations of Median Judaism? It certainly does. Ethiopian Jews are recognized by Israel’s Chief Rabbinate as belonging to the Northern Jurisdiction of Israel and are recognized as entitled to immigrate to Israel under Israel’s Law of Return. Members of other denominations of Median Judaism are no less Jewish and no less entitled to immigrate to Israel under the Law of Return. The return of the remnants of the Northern Jurisdiction of Israel was expected already by the prophets of ancient Israel. This also also relates to conversions to Median Judaism; not only are Median Jews recognized as Jewish by the Law of Return but converts to Median Judaism are equally entitled to immigrate to Israel under Israel’s Law of Return.