It's not so much that all entertainment with woke messaging is automatically dismissed by audiences, it's more so that movies and video games which offer zero entertainment value apart from woke messaging, have had a tendency to fail spectacularly.
What I mean by this is, for example, would be a movie about a gay relationship, where the gay is emphasized rather than the relationship. These sorts of hollow stories just don't seen to find an audience. You still need to build them around the basic foundations of what makes a gripping story, rather than trying to weave a half-assed, conveniently written plot with cringeworthy dialogue around a political message that you want to push.
Entertainment has always included politics, moralizing, giving life lessons to an audience, but rarely so blatantly at the expense of the story and entertainment value as today. Basically you'd have to go back to WW2 era propaganda movies to find such heavyhanded messaging.
Also, if pretty much all entertainment that is pushed out has woke messaging, it's inevitable that at least some of it will be successful due to a lack of alternatives. But this is probably in spite of the political messages being pushed, rather than because of them. They may well have been even more popular without the added, unnecessary political content that may make them appear dated and contrived at a later date, just like some old movies with obsolete ideas appear to us now. You never really want to create art and entertainment that is so obviously a "product of the times".