It's both cultural and genetic. In English when you call someone a Jew it doesn't specify and could be referring to one or the other or both.
TLDR: only Jews patrilineally descended from the patriarch Judah son of Jacob are real Jews, and those people have been dispersersed for so long that they are basically extinct and/or lost. So any Jew that realizes this and converts away from Judaism is absolved of their Jewishness.
Meaning, the only real test of Jewishness these days is: If you believe you're a Jew, then you're a Jew.
GENETIC:
A true genetic Jew is related to the parilineal tribe of Judah all connecting their line of fathers to the patriarch Judah, son of Isreal/Jacob. This line is widely considered lost though some people claim it.
The Jews of Isreal today and standard mainstream monolithic Judaism are an ethnic grouping claiming to be related to the ancient Jews by some descent not necessarily patrilineal. Oddly they require a matrilineal connection to this grouping to be considered a Jew… meaning your line of mothers is connected to them.
Other sects of Judaism, not related to that dominating mainstream monolithic Judaism in Isreal, they have their own beliefs and customs regarding their genetic connection.
When one is considered a genetic Jew in this way, then you cannot be absolved of your Jewishness no matter what religion you adopt, because you are a genetic Jew, though some of your competing sects of Jews might call you an imposter and have an argument about who is a real Jew and who is fake.
In my opinion, you're not a real genetic Jew unless you're a patrilineal Jew. There is a theory that the mainstream Jewish sect in Isreal are fake Ashkenazi European Jews who descended from the Kazars of Kazaria in the caucuses region during the the end of the first millennium… a group that famously converted in mass to Judaism when the world was going through a time of competing Christian and Muslim states, they chose a third option as some kind of political ploy.
CULTURAL:
Obviously if you're Jewishness proceeds only from adopting the Jewish religion then you can be absolved of your Jewishness by converting away.
