I think you are making an unreasonable assumption about how Jews view themselves.

Clarification question: Can you comment on where you read that Jewish folks believe themselves to be a race and not simply an confessional group?

This is certainly a view that many European racists of the Herbert Spencer variety of scientific racism/social Darwinism school of thought espouse, but that was obviously directed against Europe's Jewish population. I've never read anything about the Jewish population actively taking up this mantle.

Keep in mind, I'm assuming that you're not talking about Zionism, which is more about the Jewish nation rather than a purported Jewish race.