Considering woke culture originated in black communities in the United States, its difficult to blame wealthy elites for its use.
Ultimately, its core goal is to recognize and dismantle the covert structures within society that oppress minorities and create inequity. For that to happen, white allyship is necessary.
The fact that so many on the left are now open to woke culture is evidence of progress, and perhaps a sign of more progress to come.
While class disparity certainly affects minorities, it is primarily due to historical racial injustice. If it was purely a class issue, that would do nothing to acknowledge that black, indigenous, and people of color (BIPOC) are disproportionately affected by these disparities.
This is not purely a class issue, and it demands that action is taken to correct the inequities present in these communities.