Marjorie Ingall has a profile of Simms Taback's work in Tablet today. I'm familiar only with Joseph Had a Little Overcoat, but based on what she wrote about it, I suspect that she misses some of his Jewish messages. Writing about Joseph, Ingall says: "Hidden in the illustrations are a collaged Tevye poster, photos of different fabrics, a teeny copy of the Yiddish Forward—so much texture you could plotz."
What makes the book Jewish to her is the fact that it uses Jewish "texture" and was based on a Yiddish folk song.
As I wrote about Joseph a few years ago, the Jewish message is one of loss of tradition, urbanization, and nostalgia. Whereas Judaism was once a nice, thick overcoat, it slowly but surely eroded and morphed into an ethnic culture or nostalgia; what passes for "Jewish" at the end of the book is but a pale shadow of what there was at the beginning. That's the tragedy of the folk tale--compounded by the fact that the tragedy is lost on so many contemporary readers.