"Jews are best understood as a “large extended family” that accepted a covenant with God. Those who didn’t practice the faith remained part of the family, even if traditionally they were regarded as black sheep. Converts were adopted members of the clan. Today the meaning of being Jewish is disputed — a faith? a nationality? — but in Israeli society the principle of matrilineal descent remains widely accepted. Sharon’s mother was Jewish, so Sharon knew that she was, too. And yet it seemed impossible to provide evidence that would persuade the rabbinate."

"Sharon left the office infuriated. Her mother was Jewish enough to leave affluent America for Israel; her brothers had fought for the Jewish state. Now, she felt, she was being told, “For that you’re good enough, but to be considered Jews for religious purposes you’re not.”

...New York Times

I think the Jewish leaders skepticism comes from all the stars like Madonna who convert and then claim they're now Jewish. Converting does not make you Jewish, you're birth does.