Earlier quoted context omitted.
‘Woke’ just means, open to the idea that the way you behave may have unintended negative effects on other, potentially disadvantaged folks and it’s worth changing the way you behave in these circumstances. So also - empathy.
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Painting with a broad brush, conservatives show empathy only for people like themselves and perhaps close family and friends or a local community. Progressives show empathy towards a far broader range of people.
(I think it's no accident that cities tend to be more left. They force people to have larger and more heterogenous tribes, and the correlation between political leaning and size of tribe apparently has some power in both directions.)