My favourite JRPG series, Suikoden, had 5 games between 1995 and 2006 and are pretty political and I love how their stories have a lot of shades of grey so you can even agree with some views of the villains. There's nothing "woke" about them, it's simply just very good storytelling.
To quote
this article.
The Suikoden franchise deftly tackles contemporary philosophical, moral and political inquisitions without coming off as pretentious, convoluted or too cryptic. The individual conflicts and political intrigue are all superbly written.
So yeah, I see absolutely nothing wrong with a story being political. No matter what the subject of the story is, what matters more if it's well-written or not. But I think we can agree that "woke" is not well-written, pretentious stuff rarely are, if ever.