Again, you seem to be trying hard to blame some evil group for the self descriptive nature of another evil group.Woke belongs in the same category as words/phrases such as SJW, virtue signaller, cutural marxism and other right wing nonsense that is used to deflect from scrutiny and embed a feeling of victim culture in the perpetrator of the usage.
Social Justice Warrior was something college kids schooled in the asinine theories of Social Justice used to scream about 5 years ago. They weren't labeled that. They called themselves it.
Same with 'Woke.' Virtue Signalling might have been a label, but it wasn't from the Alt Right. It's anyone with common sense who finds people who do this pretend "show of support' thing annoying.
Black Liberals (again speaking America) used to accuse White liberals of such. So it's not an Alt Right thing.
You however are exhibiting a bit of what folks often accuse Leftist of: I.e. labelling anything you NOW disagree with as Alt Right.
There is a vast spectrum of ideas between the far left and Alt Right.
As for Cultural Marxism. Conservatives use this term across the board to refer to a strain of intellectual ideas emanating from the Cultural, and Social Science fields of study in the Universities that Centers their Study on victimhood based of group identity.
And In so far as it might be true that Alt Righter's use this term, they are not the only ones who do and there is a legitimate basis for so doing.
The trick of labelling things you want surpressed by associating it with the Alt Right will only work on those who don't know better...