In this answer, someone said they got offended when people wore crosses, especially if they didn't know they were Jewish. I'm just wondering how someone can not know what religion they follow?
In Jewish Law, a Jew is a Jew and remains a Jew no matter what actions he or she takes.
You could even say, "once a Jew, always a Jew".
That means, if someone is born to a Jewish mother (because Jewishness is passed through the mother) and is never told that they are Jewish, they are still a Jew.
Judaism is not a religion like Christianity or Islam is. One's Judaism does not depend on what they practice or believe. You can convert ten times over and you will still be Jewish. Sorry ;).
A person is a Jew if their mother is a Jew. If a jewish woman marries out of the faith and did not bring up her children as Jews they are still Jewish, even if they do not know it or practice it. And then her daughters children remain Jewish and at this point most likely they have no idea what it means to be a Jew.
In totalitarian regimes wives would not tell their husbands they are Jewish. There is plenty of people who are Jewish (in maternal line) and do not know it today. Also, it was far more common for Jews to become (forced) Christians than otherwise. I have a bit of 'Jewish DNA' and found very very distant cousins among New Mexico conversos/'marranos' descendants and in other places. With very slight probability I could be born Jewish, and if I wear a cross, then I could offend someone. G-d only knows what is hidden in us. DNA can tell both maternal line and paternal line descent, but, unless one is extremely lucky, it can only tell approximate geographical area of origin, with no meaning for the Jewish faith. By the way, every Jew has sincere (otherwise they would not upbring Jewish children) converts 'blood' to various degrees, making it more difficult to track 'legitimate' Jews based on genetics only - it is practically impossible.