It shares a word with a modern broad concept of shunning, but shouldn't be confused with it. It certainly doesn't relate to broad discrimination or "woke cancellation."
This really isn't in the spirit of HN.
"Woke" is just the latest term for social justice. There are people who don't want a society that is just but they can't say it in the open (as much) any more, so they come up with euphemisms. The previous was "politically correct."
It is too ambiguous to be about anything in particular, so we should just talk about the real issues specifically and in depth. If it is an issue to be against caste reforms, discuss that, don't just call someone woke and close the book.
It is also a bit of a dog whistle even if accidentally, since it isn't actually about any specific issue, but people can still identify that they are against it. Call something "woke" and suddenly people who never cared about the issue before will have a problem with it.
Language is weird though, the word has evolved a weird meaning and been co-opted by political agendas, so it is just nice to not drag that shitshow into real discussions as well.
There are also reasonable and good people who have legitimate disagreements about what a just society looks like and don't appreciate the "you're either with us or against us" attitude you're projecting.
For example, I can be 100% on board with treating everyone respectfully and equally under the law while still thinking it's harmful to try to erase the contributions of good people from centuries past on the grounds that they weren't good enough by our modern standards. That's the kind of thing that I label "woke cancellation", and you'll never persuade me that judging a historical figure based on our modern values is just.
I have heard people who believe we should tell the whole truth about historical figures like Thomas Jefferson, who raped a teenage slave he owned & perpetrated genocide of Indigenous people, or Christopher Columbus, whose contemporaries condemned the genocides he committed, but that isn't "cancelling" anyone: it is just no longer being willing to lie for the comfort of the powerful.
Otherwise I agree with roguecoder. Telling more of the truth about people and situations is to the benefit of history and civics. It shows us that flawed people can lead, and it shows us that our present leaders and politicians may have serious flaws, but that doesn't mean they aren't effective leaders. It just means they have stuff to work on, and we shouldn't okay whatever they do as long as it is to our benefit (i.e. the ends don't always justify the means).
If this were the goal, I would embrace it wholeheartedly. I have no problem with historians telling true stories in all their messy details, and I'm fine with removing historical figures from pedestals and showing how they were flawed humans just like those we have today.
What I strongly object to is that in most cases telling and learning from the truth is obviously not the goal: see the massive witch hunts surrounding James Webb. It was never important whether or not the accusations against him were correct, the important thing was to drag another name through the muck in order to score virtue points in modern politics.
The attitude driving most of these incidents isn't one of respectful-but-full disclosure, it's more reminiscent of people in the Middle Ages digging up and mutilating corpses to make a political or religious point.
Parents are mostly exposed to the hateful heretic-burning historical revisionism, not the careful, constructive, academic approach to telling the full story. When the kids come home saying that they learned X, Y, or Z about a historical figure, the parents assume (right or wrong) that they're being fed the hateful garbage that they see in the public sphere, so they lash out at the curriculum.
Some in the Left use that as evidence that conservative parents are hateful and (to quote OP) "don't want a society that is just", but what actually happened is that the parents were never given the opportunity to engage with the full story: they were taught the saintly version in school and then in later life exposed to the demonic version. As far as they can tell those are the only two choices they're being offered.
I think the lesson to pull from all of this is to try not to be a demagogue, and do your best to communicate in such a way that you can't be misinterpreted or misquoted as a demagogue.