> Zipcodes in the Appalachias for example.

You're overconstraining what I've said. You're perfectly right that zipcodes in Appalachias account for many poor people that are also white. But actually, you're correctly inferring that you can still infer race out of this, because you're inferring that the majority of these zipcodes are also white. Right? White people are also a race. You're correct that zip code is also able to strongly indicate poor white people. In fact, it is also even able to strongly indicate rich black people. Though you might guess not to the same degree as the overall rate is lower, but people do congregate.

Think about it in a different framing: zipcode strongly correlates with people congregating together who are culturally and economically similar.

I think this version should make sense (especially as the locality affects the culture), and that from here you can extrapolate to recognize that people of varying demographics aren't homogeneously distributed among zipcodes of similar economic bins. I part of this is easily explained by a simple fact: when people move, they like to move to where they have friends, family, or other connections.