My mother grew up not knowing she was Jewish. She was always the outcast at Catholic school; kids teased her, calling her "Jew" and if she showed up on Jewish holidays, they would say, "Why are you here? Aren't you Jewish?" It confused her for a long time. She thought maybe it was because her last name was a very unusual Italian one, and her family was not religious (my grandmother had a Catholic Bible in the house, but said that statues were "idols" and crucifixes "are bad luck". I lived a sheltered life, and so my mom's family were the only Italians I ever knew till I was older (I was very shocked when I was a teenager and found out that yes Italians DO eat pork and DO wear crucifixes!)
My mom converted to Torah Judaism when she was 19, a few years before she met my Dad and married him. For years she was the ONLY convert she knew. Then in the 1980s I got interested in genealogy and to make a long story short, learned through a distant cousin (and the records he got from Italy) that my mom descended from Italian Jews who originally came from Spain at the time of the Spanish Inquisition.
That explained a lot of questions I'd always had, such as why grandmom would light two candles on Friday nights after closing the curtains, and why she refused to eat pork or let anyone in her house bring it in. I guess she was handed down just a few Jewish customs but not enough so would know she was really Jewish.
Grandmom also used to tie a red string to the handle of a new car or house, saying it brought "protection". I always thought that was an Italian thing, I later learned its from the Kabbalah. Spanish Jews were heavily into Kabbalah, so that explains that, too.
So anyway, I grew up being taught my mom was a convert, but I found out later she really wasn't, but was technically born Jewish. I still regard her as a convert because she was not raised Jewish.
Talk about someone with an identity crisis!
But anyway its because of all this that I identify as BOTh Jewish and Italian, even though by religion I am only Jewish.