You are absolutely right! My children are ethnically half-Jewish, although their father is not religous, and I have always told them that they could go either way-- same God, different holidays, their choice. ;)
That's neat. The rabbi of some of my Californian cousins was raised both Jewish and Irish Catholic. He had both a bar mitzvah and a communion (confirmation? I might be mistaken as to which is which) and after he did a tour with the Marines, he had a choice between yeshiva and seminary school. Chose yeshiva after a long hard decision, but I've always found the idea of Rev O'Connor very amusing. He's by all accounts an amazing man too, all the better and his faith in G-d all the stronger because he was raised with both backgrounds.