So what should be the word we use for “media that depicts positive social ideologies?” Apparently “woke” includes the definition “while being super preachy about it.”

For a lot of people it does, yeah. I don’t know if the best solution is to run away from the word, though – like you say, it’s good to have a word for this stuff, and a different word is just as susceptible to being tainted by conservative strategists.