If you move to a rich zip code your child goes to a well funded school, hangs out with rich kids behaves like a rich kid. Moving to a rich zip code (and supporting your child’s education) is a fantastic way to get your family on the path to generational wealth.

It really is. In fact there's some good studies that suggest that this is even true with race, where you don't need to move zip codes but simply move schools (a la "Everybody Hates Chris"), if the kids are young enough.

But clearly the causal connections here are not zipcode, but schooling, culture (or rather the knowledge to understand and navigate a culture), social connections, etc.

No, that does not make it causal.

1) Causal relationships are directional. Which then follow your own logic. You can reason that it is directional because you can see that there are many ways to get into rich zipcodes without being rich.

2) You can find many rich people that don't move into wealthy zip codes.

So actually, it is just correlating. If we use Judea's ladder, then it is causal in that sense, but that's the lowest rung and not what we'd call causal in a colloquial (or even statistical) sense other than to be pedantic.