Definitely, and that will make it harder to detect, but if you suspect it's the case and manage to sue, it becomes pretty obvious. They'll have a tough time explaining to the court why they chose to target their apartment ads to, say, people who buy sunscreen. And trying to pick a more subtle demographic will come off as even more ridiculous.

I can imagine seemingly justifiable proxies. Targeting people who buy lawn care products and people who buy wild bird food is both arguably enriching to the neighborhood (birds and grass look nice) and probably correlates to WASPs fairly well. I remember the bird food example being brought up as something that credit ratings are influenced by, but I don't remember the source.

Edit based on sketchy memory: s/organic/wild

Those demographic correlates of race are already illegal as substitutes in similar domains (like qualifying for a mortgage). If they aren't illegal already for (e.g.,) landlords, it seems like an easy expansion of current regulations.

One of the measures is a public archive of all ads in these categories and their targeting.

That allows third parties to analyse ads for any remaining bias.