Well I think we have to take "woke" to mean the most plausible
worst version of this ideology; or else we'd just name it charitably. Ie., the OP comment is nervous about being associated with the type of thinking i'm talking about.
It's entirely fair to say that whilst accommodating and judging people individually we need to account for that person's particular difficulty in first being judged in this manner -- because we, the judger, may be unable to properly understand their situation; and likewise they may not be able to argue their case, state their need, etc.
The problem enters when we take the goal of our project to actually be removing such "prejudices and obstacles" and, not rather, the empowerment of each individual. The former is an often optional detour to the latter.
Consider, for example, the most effective civil rights president in US history (LBJ) was a racist: did we need to solve his prejudice first? Would that have done anything positive?
Wokeism, if it means anything at all, I think has to be identified with this ends-means confusion. It's raising to the status of an end in itself the elimination of (minority) group hatred, (minority) group prejudice, etc.
This a deeply confused project; and routinely gets in the way of the actual end everyone cares about: each person, in their own particular situation, being able to live the way that best suits them.
If I read the message here correctly, the woke-dissenter is saying this: "My difficulties are particular to me, and all I want is to be able to solve them. I don't want to participate or "ally" with a society-wide war against the possibility I will be misunderstood or mistreated; rather I simply want the rules (,tools, practices) in place to empower me when I am."
Wokeism is the political incarnation of New Atheism, or likewise Evangelism: first we fight a total war against The Sins of The Mind themselves; and then, much much later, we help people in their particular situations.