I agree that teaching kids to be critical of one sliver of reality, while uncritically absorbing anything from another sliver is a pedagogical crime. What we ought to be teaching is critical thinking.
It’s worthwhile to teach children the true history of progress and ask if perhaps there isn’t a better way.
Complaining about “wokeness” is to be willfully stupid. Your kids will find out the truth, even if you try to hide it from them.
The truth of that depends entirely on whether that civilization's "success" is something that either can or should be sustained, and that's the assumption that most "woke" people challenge. Very few seek to tear down any part of it without having carefully considered whether it really contributes to long term success.