I'm not sure what you mean by "real woke" but based on the Shutting Detroit Down referece, I'm guessing you mean something thats in the same vein as Johnny Cash's What Is Truth.
Have you listened to the new Highwomen album? Brandi Carlile, Natalie Hemby, Maren Morris, and Amanda Shires would be one place to start.
Margo Price (with her Pay Gap) would be another starting point.
Or listened to any Crystal Shawanda and her Native American themed songs.
Clear Isabel by Aaron Watson is an other example.
Buffy Sainte Marie is another activist country artist, although she has moved to different genres recently.
In his day, Woody Guthrie was considered country.
There are very few country artists who built their career around activism like Pete Seeger did (when he started out, Folk and Country were the same genre, the split into two genres came in the middle of Pete's career (partially because Pete's politics scared record executives.))
But the common person getting the short end of things is an old country theme. The theme in Shutting Detroit Down is and old theme in country music and is expressed in a variety of songs, older and newer.
Bob Will's song Take Me Back To Tulsa had the line "darkies grow the cotton, white man makes the money", which has been changed by other artists to "little man grows ... big man" and other similar pairings. And its just a quick little line, not the core of the song, but the realization that The Man is screwing the common guy is there and in other songs.
The Common People Get Screwed is a background theme in all kinds of country music. (Sixteen Tons, Dark As A Dungeon....)
Feminism in various forms has been a feature of country music for quite a while.
So has gun control (Conversation With a Gun, Tex Ritter)
Two things about country music.
One, the industry has been and is scared to death that listeners will boycott or such. But the truth is that the listeners are much less monolithic than the industry fears. It Wasn't God Who Made Honkey Tonk Angels was ignored by the industry, it was banned from the Grand Ol Opery, but the listeners still make it a hit. There was a similar response to Loretta Lynn's The Pill and to Johnny Cash having Pete Seeger on his (Cash's) TV Show. Willie Nelson's Cowboys Are Frequently Secretly Fond Of Each Other was ignored by the industry, but not the listeners, they listened and live moved on, no uproar. Casey Musgrave's Follow Your Arrow. The industry has always been chickener than either the artists or the public.
Two, the songs don't follow any party line. They tend to reflect real people in real situations, which is way more complex than the THIS SIDE/THAT SIDE view of issues. And there is room in country for both sides. Johnny Cash sang both Ragged Old Flag and his Singing In Vietnam Talking Blues.
Does that answer your question?
One more thing, the new Songs of Our Native Daughters album is from the old old string band genre (proto BlueGrass), and definitely a good album (Polly Ann's Hammer is one of my favorite songs). Rhiannon Giddens, Kia Kater and others are going back the roots of string band music and African American roots of country music, different than blues, but back back in the day, African American cowboys and musicians added to the Western/Cowboy music tradition. And there are contemporary artists who are exploring that genre, bringing it forward and using it to express activist ideas.