I’ll call this a swing and a miss — it was good sci-fi, an interesting twisty story, but had as much to do with “believe women” as “Chain of Command” had to do with “believe men”.
The fact of the matter is that many ST:TNG episodes, both “Remember Me” and “Chain of Command” or even “Frame of Mind”, play with the idea of perspective and truth. And if you pay close enough attention, you’ll realize that the overarching theme is that perspective is not necessarily truth.
It just so happens in “Remember Me” that everyone except Crusher is delusional, and in “Frame of Mind” Riker is the one suffering from delusions. “Chain of Command” does something even more interesting by having Picard deny the delusion he sees (five lights when there are only four). But none of this has to do with any sort of social justice warrior messaging.
That being said, it is great fiction because it allows us to map ourselves onto it, regardless of point of view. Someone who is an SJW can see it as “believe women because they never lie”, and someone who is an MRA can see it as “not all men are misogynistic assholes since Picard believed Crusher”. Its utility actually comes from its ambiguity, much like how “The Hunger Games” was written as a diatribe against the War in Iraq Republicans, but it can be interpreted as a diatribe against Big Government Democrats.