Great question because it matters so much. Like all words which have many meanings, the word "Jew" also has many meanings. A Jew can be a member of Judaism (whether born into it and confirmed through a bar/bat mitzvah or a convert), but it can also be a reference to somebody from the Southern Kingdom, the tribe of Judah itself, and also somebody who is genetically Jewish... whose ancestors trace back to, say, the Southern Kingdom after the split? One can be genetically Jewish, be an atheist, still do a Passover Sedar every year even though he doesn't believe the stories... and still be Jewish by not just genetics but by practical identity. And that has been my connection in this thread... religious and non-religious Jews are identified today BY RELIGIOUS practice. Sounds odd... but like I said, one of my best friends is a secular agnostic Jew who makes darn sure he gets to his secular dad's home for Passover dinner where they eat unclean meats... but STILL tell the story and go through the order of events like the religious Jews do.
Their practice identifies them.... whether secular or religious... and the "you don't have to keep Passover" pitch by the Christians is taken as a threat NOT by me... but by THEM.