It is and it isn't. Allowing the word 'woke' to be hijacked by the liberal white middle classes and then used against them by an opportunistic right-wing was a huge mistake in retrospect. There is a conflation here between 'woke' as explained by Black people and 'woke' as co-opted by dungaree wearing kids in their twenties with rainbow badges and the inability to think themselves out of a paper bag.

As a movement grows - it must be careful about which allies it allows to utilise the language. Woke rapidly became a pastiche of what it once stood for and that has further disempowered Black people. If all it took to be 'woke' was putting a BLM sticker in your window, we would've solved racism by 1967.

In that vein, you might enjoy this https://medium.com/lucid-nightmare/white-girl-from-oxford-ends-racism-50f5b3624aba