I’d recommend the twitter feed of @doctorow or @waxpancake, where there are a lot of educated (and uneducated) folks weighing in. As I understand it, there’s a four-factor test, only one of which hinges upon advertising. And even then, it doesn’t say advertising can’t enjoy fair use, only that it might receive “less indulgence.”
Given the strong pro-feminist / anti-sexist message of the video in relation to the original, it’s hard to imagine what would pass the bar if this doesn’t.