Race is the wrong word in the modern American context. Jews aren't a race in the sense of black vs white.
Jews are, however, an ethnicity - much like how you can be ethnically Navaho or ethnically Basque. It's a matter of being part of a community of people with a shared culture and ancestry. And yes, beta Israel and Ashkenazim are both ethnically Jewish.
Let me make sure I understand you: your argument is that any self-consistent Jew cannot make an image of anything that can be compared to religion? So anything grand that people find meaning in that requires sacrifices with weird superstitions and rituals.
So no flags because of the religion of nationalism, no money because of the religion of money, no On Food And Cooking because of the religion of French cuisine, and no pictures of Rossini because of the religion of opera?