If it helps, consider this analogy.
You, “Vegan pizza is a smart idea.”
Conservative, “Vegan pizza is a stupid idea.”
Is one of you necessarily lying? Of course not. There’s a difference of opinion which may or may not be justified. Vegan pizza is neither objectively smart nor objectively stupid because those terms are subjective by definition; the truth of both statements is therefore subjective.
Woke as a pejorative doesn’t mean stupid, but it is subjective in the same way that stupid and smart are.
~Max