Question

Rabbi, not long ago I had a discussion with an educated secular woman about Judaism. She doesn’t believe in God, etc., so she lacks the basis for Torah and commandments, but that wasn’t what the discussion was about. 
I raised the issue of Jewish law, or more precisely the principles of Jewish law that were the essential defining characteristic of Judaism throughout history, and she challenged me as follows:
1. Why take an essential characteristic of Judaism דווקא from one point on the timeline, which in any case was also a relatively late point, since the Jewish people existed even before the Oral Torah?
2. According to her, Judaism is shaped by how society sees it and relates to it. That is, throughout history the Jewish people understood the observance of Jewish law differently, and from that it follows that there is no unambiguous defining characteristic of Judaism. It is hard to define, and therefore one could also argue (as she did, and she was consistent about it) that if society defines a person who identifies with Jewish history as Jewish—even if he is actually a Christian—as long as he identifies himself as a Jew, then he is a Jew.
I’d be happy to hear your opinion and a more detailed explanation. 
Thank you very, very much.