So, why would Jews NOT accept her children as Jews??
Not sure I understand your question. If she raises her children as Jews within the Jewish community, that means in the context of Jewish education and Synagogue membership, for the kids not mom, they will.
A Jew is someone born of a Jewish mother, or who converted. Paltrow's mother wasn't Jewish, and Paltrow never converted. Ergo, Paltrow's not a Jew. Paltrow has, to my knowledge, not indicated that she will convert, or that she will convert her children. So her children aren't Jews either.
The equivalent would be someone born in Mexico, to Mexican parents, whose parents raise him with American culture and give him civics lessons in American history. Such a person might know a lot about America. But, without naturalizing, he wouldn't be an American.