I always thought they should have called them “authorized” activities and businesses. The optics wouldn’t allow it, but it would have been more accurate all around and avoided these misunderstandings.
I think it's more than just optics, though. If they were called "authorized" businesses, it wouldn't just look bad - it'd be blindingly obvious why the specific set of shut down businesses should be responsive to public pressure and desires, rather than staying at some fixed level until public health authorities say otherwise.