Nah, I'm thinking of my type of SJW music.
You don't get to define what is and is not "SJW music". Assuming such a category even exists– and that's an assumption I am not willing to grant– it would probably actually be Lady Gaga or something, not "post-emo-Jesuscore" or whatever it is you're futilely trying to plump here.
So what else would describe music from bands that write long liner notes in their vinyl records about things like gender oppression and heterosexual white male privilage and hand out posters like
this at their shows and is almost exclusively played by and appeals to middle class educated white people who have no problem spending $30 on limited edition colored vinyl versions of records released, more inflated prices for band shirts and hoodies, and at shows get very drunk off $5 a bottle beers and then go mosh the f[inks] out? Sounds like the epitome of SJWs to me.