Do you know a lot of "woke" people who aren't otherwise on the left? I don't.
Do you know a lot of "left" people who actively speak against the "woke" crowd? I know very few. Almost all of them who speak on the topic, speak in unequivocal support of "woke" ideas and talking points.
If "the left" doesn't want to be equated with the woke culture, they should publicly and consistently disown it. You know, in the same manner as they demand that conservatives disown Trump and his crowd to not be counted as racists.
It's in everyone's power to start extinguishing the extremes. Until then, I'll take silence on your nearest extreme as your tacit approval of it.