Is there any conventional wisdom in the stats community about how far to trust these kinds of adjustments?

In my experience there's no general answer other than the observation that if people did NOT adjust for confounders, it's usually a very bad sign. But if they did, you actually have to go read the paper and form your own opinion on whether their adjustments look reasonable, whether they did them correctly, whether they picked the right confounders (or just grabbed whatever characteristics they had handy), etc.

Typically people don't adjust properly because it's against their incentives to do so.