Yeah, I'm not saying art has to be politically neutral. I define "propaganda" as a message that's produced solely or mainly for political reasons, whereas a story is artistic if it's produced solely or mainly for artistic ones.
The problem with woke "art" is that the producers are hired not because they have artistic talent, but because they excel at getting a political message across. Shaw, Dickens, Woolf, and the rest had artistic talent, regardless of their political motives. They weren't thinking just of their political agenda when they wrote. They were crafting their characters and plot, with aesthetic standards in mind.
That's all I ask. It's not so hard, but the Twitter mobs and PC, cancel culture are taking over Hollywood, provoking an exodus from LA. Luckily, technology is democratizing the entertainment industry so real artists can have their say with few if any intermediaries. The downside is that the true art often gets lost in the informational deluge.
So I don't think your reductio criticism goes through. I should say, though, that another sign of propaganda is if the fake art is defending the status quo or a dominant institution. True art is often rebellious in that it's produced by social outsiders or members of an underclass who don't have anything to lose, so they can afford to focus on aesthetic concerns.