If I may, I would say that "woke" is, most broadly, the cultural manifestation of 'equality'. More specifically, it refers to the basic respect that 'equal' people owe to one another. There is respect that must be earned, but among equals there is a fundamental level of respect that all must afford to all. It has been expressed in Liberalism in the maxim that everyone's liberty 'ends at the person and property of any other person'.

Historically, liberty and equality have been identified in Liberalism as the 'twin pillars of justice' for a just society. Of late, the conceptual and practical limitations of that approach to justice are being exposed. The result is a crisis in Liberal society. So what we need is a better approach to achieving a just society.

Here is an alternative to that 'old' Liberalism: "A New Liberalism" (here in Medium, but not--for the benefit of any 'guest readers'--behind the paywall). In it liberty is maximized, but as a product of justice, not part of its foundation (or its source, or its predicate, etc.). 'Equality' is dismissed as an unnecessary complication: all that matters for justice is that the beings involved are humans. A Liberal society that came to be governed by this New Liberalism would not have to change one bit structurally, but its functioning--its effects on people--would be transformed (most obviously in the economy).