You ask what the alternative to being "woke" is. And the answer is: to be charitable and assume the best of people until they demonstrate otherwise.
The problem with being "woke" even in the original definition is that it sets up a trend of unhealthy paranoia and suspicion. When lack of such suspicion had extreme consequences (like dying), it was perhaps warranted. But today, the psychological burden is arguably far more damaging, on average, than the things one is trying avoid, and there is a great risk of triggering reciprocally hostile behavior by assuming hostility where there is none (which then is classified as "aha I was right all along!" instead of "I was antagonistic due to my suspicions and provoked an antagonistic response").
This isn't to say that we shouldn't as a society find systemic problems and actively fix them. We absolutely should! But stressing constant individual vigilance instead of a default of a positive, good-natured outlook coupled with decisive legislative or grass-roots action is observably bad for social cohesion and even for understanding the situation (as paranoia-driven bias leads one to exaggerate real but small effects and imagine malign motives where none exist) while delivering few remedies that actually solve the systemic problems.
Almost every successful advance in tolerance and justice has been delivered in connection with a unifying, uplifting message. As a social movement, "wokeness" is divisive and depressing. When necessary for defense--absolutely; otherwise, even in the best interpretation it's best saved for emergencies and analysis, and shelved when interacting with others in all but the most extreme circumstances.
If you take the progressive extension of "woke" (widespread in the late 2010s) to include popularizations of critical-theory inspired ideas and the remnants of social justice warrior attitudes, it gets worse yet: now you have enforced tribalism, shaming, original sin, impossibility of being freed from original sin, and all the other emotional baggage of shame and guilt that would make a hardcore Protestant evangelical proud. If you just step back and observe how religious people behave in that pressure-cooker of impossible expectations and severe judgments, you find that, actually, they are routinely terrible at doing what Jesus would do. They're judgmental, hateful, closedminded, etc.. Ideologically, it's perplexing--isn't that backwards? But psychologically it makes perfect sense. And if the progressives recreate the same emotional maelstrom on their side, guess what? They're also routinely terrible at being actually inclusive, welcoming diversity, and a bunch of other things they claim they want.
Human beings have a bunch of weird quirks. As frustrating as it is, you can't really create a better society without understanding them and working around them. Original "woke" is okay for emergencies, but problematic for the long haul. Progressive "woke" provides lots of ways to cause harm while feeling self-righteous about trying to cause good, and tools that actively interfere with being able to tell whether any harm is caused or whether any good is being done. Conservative anti-woke is such a messed up bundle of reactionary regressive nonsense (in practice--sometimes they espouse sensible principles, but the proof is in the pudding, as they say) that I won't even bother talking about it here.
Edit: here’s an example of some psychologically well-grounded advice that is almost dimetrically opposed to the kind of thinking patterns that most naturally arise when one is mindful of being woke: https://getpocket.com/explore/item/how-to-thrive-when-everything-feels-terrible; this is the kind of thing that suggests that “woke” is at the very least challenging to adopt while maintaining personal well-being and cognitive health (and if we’re going to advocate for it, we’d better also give people the cautions and the tools they need to manage the possible negative effects).