Memes

If anything it would be more a 'tu quoque' fallacy than whataboutism, because the latter tries to shift the attention to an unrelated topic, whereas here it is occupying land both times.

It certainly weakens the criticism, because the robber in your example might do the right thing, but if they really opposed robbing, surely they wouldn't do it themselves? As you said, it makes them a hypocrite, and makes you question their motive for measuring two cases with a different yardstick.