Well the Reform Jews (the ones we beat this time of year, they were called Helenists then), hold that any Jewish ancestry makes one Jewish. And certainly they don’t mind if someone isn’t following halacha. And given the ways genes tend to flow over time, and that some Jews have always been wandering off getting into mischief (and being into mischief, it does encourage gene flow). You let one guy lose in a population and 3000 years later, everyone is related to him (do the math, his descendants come to something like two to the hundreth power after a few millenia).
So to show we aren’t “sore winners”, we’ll use the Reform’s definitions of Jewishness (indeed, being so unfussy, they’ll probably want to extend it back to Noach, rather than just to Avraham)– and you can assume anyone you want in the world is Jewish.