It doesn't really matter what label is used, whether you call it 'Critical Race Theory', 'Woke', 'IdPol' or whether or not The Graun tries to put a positive spin on it or not.
And god knows what rock you were living under last year if you didn't see any of the discourse around 'White Privilege', 'Unconcious Bias', 'Defund the Police', 'Robin D'angelo's White Fragility', 'Ibram X. Kendi's Anti-Racism', 'Cancel-Culture'… All of which are part of a particular school of thought which a lot of people will group together as 'Woke'.
Being sceptical of that school of thought is not a 'dog whistle'. The majority of people, including the majority of ethnic minority people, want to emphasise universal human aspects of life that unite us rather than raise the salience of racial divisions to create conflict - especially given that all progress towards racial equality ever has been born of seeing commonalities.
Most people are not racist, most people want to progress towards a world where race is as inconsequential to someone's ability to achieve their potential as their eye colour or hair colour. It's hardly surprising then that most people are suspicious of a school of thought that gives absolute primacy to racial identity and seeks to sow division between racial groups for the benefit of a small group of self-interested grifters.
It's not just a race thing either, it happened when the woke Twitter ghouls descended on the murdered woman in South London before her body was even found to ensure that her death could score them points on Twitter by making infographics about patriarchy. Unfortunately, the grifters have a massive amount of power within Labour's activist base - and until they manage to expel them Labour are fucked, unfortunately.
To help you understand what I'm getting at, You know how Tommy Robinson turns up at whatever terrorist tragedy occurs and uses it to advance his own political agenda? - That's how most people feel about 'woke' when they do the same thing but for their own warped ideology.