Is it a sin to claim to be jewish when you’re not?

I’m about as much a protestant-raised atheist as they come, and will start this with saying I’m pretty sure I’ve never met a jewish person irl – according to wikipedia, there’s exactly three synagogues in Finland altogether, and I’ve never lived in one of the cities that houses one of them. This being said, one night I was getting drunk at the park in random company as one does around here, and encountered a guy one could classify as a pizza cutter – all edge and no point – who among other things kept making antisemitic jokes.

This annoyed me and I told him to cut that out. Odds are he has never actually met someone who’s jewish irl, either, and to defend himself he halfway shrugged and said it’s not like there’s anyone here who’d be personally offended that, anyhow. I asked him why he’s so sure of that.

Both being drunk, I’m not sure whether I worded myself oddly or if my tone of voice was different from the intended, but he misread my question to imply that I was jewish. Not being sure how to correct him without losing face, or losing the footing I had just gained in startling him out of saying stupid shit, I opted not to correct him. Which was a win at the moment but now there’s a band of park-drinking folk out there who think I’m jewish and I’m not sure how or whether to correct them.

I don’t even know if judaism has a definition of sin like christianity does (or to word it better, whether it’s anything similar to that one), or whether it covers anything gentiles are up to, but I just wanted to ask whether I morally should come clean about this to a crew I don’t even drink with anymore.