Thanks for pointing this out! To improve specificity, I think we need to explicitly add in the requirement that the overgeneralization is applied in the service of looking at social justice issues from a left-wing perspective. This is already implicitly understood in our everyday usage of 'woke' (i.e. it is generally not applied to the right, no matter how abnormal or outrageous, and it is generally not applied to economic debates, as in people won't think of old-school socialists as woke).

In fact, the examples you gave demonstrate how the right can equally fall for the same kind of logical fallacy as found in wokeism. This really needs to be pointed out, I think.