About her Jewish identity (or lack of it) here is the explanation in article in the Jewish Women's Archive:
"The importance of Judaism and Jewish culture in Hellman’s life is ambiguous. She rarely wrote about Jewish themes in her plays and certainly never from the stance of an observant Jew. To the extent that leftist intellectual liberalism has been marked by a Jewish presence, Hellman fits into that tradition comfortably. In her memoirs, she addresses her Jewish heritage as part of a cultural background. Even here, she notes that the fact of her Jewishness didn’t fully hit her until she was confronted with antisemitism in the national socialism of Germany during a trip there in 1929. Being a woman and being a southerner seemed more important texts of identity for Hellman than being Jewish. In interviews, she remarked that southern Jews tended to downplay their Jewishness. If one only read Hellman’s plays, one would not necessarily guess that she was Jewish. And, while her memoirs do address this part of her identity, it is clear that Jewish life was not central to her sense of self, at least the self that was an artist and the self that she constructed in her memoirs. Indeed, Meyer Levin felt that Hellman was instrumental in blocking the production of his dramatization of Anne Frank: The Diary of a Young Girl because Levin’s play was 'too Jewish' in its depiction of Jewish religious practices and in its articulation of Anne Frank’s Zionist sympathies."I find this description to be too insistent -- its attitude seems to imply that she had an obligation to have a strong Jewish identity. I think she accomplished a great deal, and I admire her. And I think there's room for a fully secular Jewish life without being Jewish.