Being “woke” means being aware of social injustice

From the left-liberal perspective, sure. But Libertarians and far-right theocrats have also employed the term as a positive self-descriptor, insisting that they had a more enlightened and historical view.

Being anti-woke simply means that you outwardly deny said systemic racism

Racists have employed the term to mean they blatantly reject the history put forward by liberal scholars. It’s a form of political denialism, not unlike climate change denial or holocaust denial.

The irony is in how reactionaries will embrace the term and its synonyms positively - Dark Enlightenment, Great Awakening, Objectivism, “Wake up Sheeple!” - to imply they’re the ones who truly understand the victims of state persecution (inevitably, rich white cis/straight men).