Well maybe you shouldn't, because back in the '90s, when the phrase that meant the exact same thing back then was "politically correct" and not "woke," I remember hearing all about how a black station commander, a female captain and a black Vulcan were all "politically correct" and it was ruining Star Trek, which was never like that before.
Edit: I wrote 'white' instead of 'female' because I have slept about an hour all night. Yay me.
Nah, no one would call the Michael Bay Transformers movies “woke”. We all know it’s about displaying progressive values.
If you want to say something’s badly written, you can just say that, and avoid aligning yourself with bigots who flip their lid over a black little mermaid.
Acolyte's writing is fine. There's the occasional bout of wooden dialogue, there's stuff you can nitpick such as "why does only Osha notice those moths" but OTOH you could also not miss the forest for the trees. The big-picture stuff is where the writing shines: Through various twists and turns and reveals and different characters having different knowledge and versions of events it explores the general topic of Jedi vs. "off-brand" (non-Sith/Jedi) force users from all kinds of angles as the viewer considers all those different perspectives before actually knowing canon Jedi policy regarding the... fuckup, let's call it.
That all that was deliberate and very well done, but it also requires you to watch until at least episode 7 (8 isn't out yet).
Meanwhile there was a deluge of 1/10 reviews on imdb, before the first episode had even aired, presumably from 4chan and kiwifarms snowflakes getting triggered by "there's going to be a good amount of female characters" and "we casted Abigail Thorn".
That all said, yes, the series is woke: It is aware of systemic injustices. It explores them. Nothing to do with our world though because there's neither Jedi nor other force users and as such they can't have a relationship. You could read it as an allegory to possibly a thousand things, or you could view it as an exploration of the general mechanisms behind such conflicts, your choice.
That, right there, is good leftist writing. None of that sappy idealist Discovery crap but a materialist exploration of fundamental mechanisms.