What I cannot understand is: who cares? Why do people want to know? Of what relevance is this issue to being Jewish?
The Zionist founders of the State of Israel wanted a nation 'like all other nations', and so make determinations based on their own logic and politics. There is little difference whether the government defining who is a Jew is France, Indonesia or Israel.
There are many Christian, Muslim, and some other religious adherents who are first-class citizens of the State of Israel. A person need not fall unbder the 'right of return' to become a citizen of Israel. 'Citizen' is not a religious category.
The traditional Torah definition of a Jew transends the usual categories of religion and ethnicity, and the Torah will always be determinate in the end.