While SBUX has all that data, they would only see their own data.
Or just... the fact that the company is still doing it. That's the other thing that's weird to me about this study: surely Starbucks itself has already studied and worked out the calculus that the PR effect is a net positive?
That is: it's hard to rule out the possibility of this being just coincidence.
The problem is the lack of randomization.
We can't know if something else Starbucks did at or around the same period caused the drop. E.g. the initial protests themselves upsetting customers in the first place or a change in pricing/promos by itself or a competitor. Maybe Starbucks jacked up its prices (or others starting discounting), which is why the public disclosures don't indicate the relative drop in traffic.
But "The decline in visits is around 84% larger for stores located near homeless shelters." is quite damning.
Some don't, but on average, it can be a net positive.
It's the kind of thing you need a scientific study with randomization to tease out. You can control for all the confounders you want, but you can never control for unknown/difficult to estimate confounders, like human emotion.