I think it's very easy to claim 'woke' with modern star trek, but I think the issue is that politics used to be more tightly wound into the plot in that they used to express leftist viewpoints in a natural way that served the plot. The episodes were well thought out and were rich with allegory and metaphors.
Now the political views have remained largely the same from before, but the writing has suffered to an extent that things feel forced and no longer serve the plot in a natural way. It's less thought provoking, and more "here's the moral of the story". Which for better or worse only really underscores Star Trek's leftist views.