Jewish by birth
...If one of the parents is not Jewish, the rule is that the child takes the status of the mother (Kiddushin 66b, Shulchan Aruch, EH 4:19).
This is what I was always taught. My father's mother was a secular Jew, which means my father, who was a lifelong, passionately outspoken atheist, was Jewish. And that is how he identified.
My mother had no Jewish ancestry, so I am not Jewish by Jewish law. But I would have been considered Jewish in Hitler's Germany.
Here in NYC, I know LOTS of secular Jews. And in my extended family, I have celebrated holidays with secular Jews.
In my daughter's social circle, there are 3 families of kids in her grade who identify as "secular humanists." This is important to me because in her mix of friends who identify as Catholics or Methodists or Muslims or Hindus, I want her to know other families "like us." Two of those three families also identify as Jewish.
The parents of one of my daughter's best friends invite us over for latkes and the candle lighting for at least one night of Hanukkah, self-identify as Jewish, and self-identify as atheists.
On a lot of levels, I think the secular Jews really know what they are doing. They keep the ceremonies and traditions without shame or embarrassment or excuses. Unlike those secular families who apologetically decorate trees in December and color eggs in the spring, they claim the culture and the traditions that they pass on through generations, without buying into the religion. And I believe that family traditions, passed down through generations, are something that most of us crave.
Even if we don't admit it.