Judaism

Rabbi, I recently had a discussion with an educated secular woman about Judaism. She doesn’t believe in God, etc. Therefore, she lacks the foundation of Torah and mitzvot, but that’s not what the discussion is about.
I raised with her the issue of Halacha, or rather the principles of Halacha that have been the essential characteristic of Judaism throughout history, and this is how she elaborated:
1. Why specifically take an essential characteristic of Judaism from one point in time, which, incidentally, was also a relatively late point, since the people of Israel existed even before the Oral Torah?
2. Judaism, according to secularism, is shaped by how society sees it and treats it. That is, throughout history the Jewish people have perceived the observance of Halacha in different ways, and hence there is no unambiguous characteristic of Judaism. It is difficult to define it, and therefore it is also possible to argue (as she argued, and she showed coherence in doing so) that if society defines a person who identifies with Jewish history, even if he is a Christian at all, as long as he identifies himself as a Jew – he is a Jew.
I would love your opinion and details.
Thank you very much.