The shawl is symbolic of the Jewish tallitt, a prayer shawl worn when Jews go to synagogue. When a Jewish person puts on the tallitt, he is wrapping himself with the commandments of the Bible. Critics also see it as a "transitional object" between a mother and an infant. Rosa, Stella, and Magda are like infants who need a mother, since they are suffering such deprivation. Wearing the shawl is their defense again the losses they have suffered.
All of this is then connected to the theme of survival. It's a struggle each day just to live through the day. Rosa gives most of her food to Magda, but Stella cares more about her own needs than Magda's. Magda looks to the shawl for comfort when she knows she must be quiet. As Rosa watches Magda be thrown into the fence, she must decide whether to go after her or stay where she is and survive. She muffles her scream by putting the shawl over her mouth.
The details of the story, important as they are, are not laid out according to any plan or scheme. We learn in the first four paragraphs that Rosa, along with her young daughter Stella and her infant daughter Magda, have been on a forced march, and that spectators have lined up along the way as the marching Jews have gone by.
With paragraph 5, the scene shifts to the confines of a Nazi extermination camp, which is not named. Ultimately, a German guard murders Magda by throwing her against an electrically charged fence. Ozick presents these details as the major character, Rosa, perceives them—not as she sees them and remembers them in outline, but as she receives impressions about them. This is the symbolic meaning of the "shawl." The result is that we experience the story as it not only affects Rosa but comforts her as much as possible within the confines of what happens in the story. Unless she perceives it, it is not included in the story.
To pigeon-hole the idea that the shawl symbolizes any one type of religious ware, might narrow an interpretation and dilute the true themes of the story. While it is true that there are various themes to stories, the more limiting symbolic objects stand as symbols, the less focused the energy of the story. Even if you remove any references to a German concentration camp, the full effect of the story is not marginalized or mitigated. Oppression can happen anywhere, and we are comforted by things as best we can.