Symphogear X RWBY is the fic.
Symphogear is an anime where girls done ancient magic armor powered by their inner song to fight monsters called "Noise" that can't be harmed by convention weapons and the moment they touch a human said person becomes nothing but a pile of carbon dust. So imagine a big glob monster either piercing and killing you as your dead body turns to a pile of dust, or it hugs you as you try to break free as you scream for your life as your body falls apart.
Thanks to a mobile game the series lore gained an item called the Ghallahorn (i.e. an object with the name of the legendary horn of Norse mythology) that can send Symphogear Wielders to parallel worlds to take out various dangers, namely a stronger variation of Noise.
For this fic the horn sends to Wielders to the world of Remnant during the Beacon era and the end up in Patch where they meet Team RWBY. They catch a news report of the Noise attacking and neither Huntsmen Weapons, Dust, nor even Aura protects people from becoming carbon, much to the horror of Remnantians.
The Wielders quickly take out the Noise, but this is only the start of the problems. Tsubasa, one of the Wielders and currently stressed and burying herself in work (a bad habit of hers), advises Ozpin to cancel the Vytal Festival, and Ozpin agrees. Pyrrha then tries to talk to Tsubasa in the hallway, but Tsubasa' icey attitude is not doing her image any favors and it only gets worse when Pyrrha tries to talk about Aura. Tsubasa does not know what she is talking about, and Pyrrha tries to show her by unlocking Tsubasa's. Now, while other crossover fics have unlockings happen without much issue, this fic plays it VERY differently. Here....Tsubasa shows NO Aura. Pyrrha is shocked and very concerned because "No Aura = No Soul". Tsubasa gets away, and then CINDER approaches Pyrrha. Pyrrha tells Cinder Tsubasa has no Aura, and Cinder uses that to stir the pot and plant seeds of doubt into Pyrrha.
Now the kicker with today's recent chapter. Pyrrha tries to bring up the No Soul thing to Ozpin, but he brushes her off and tells her the Vytal Festival is cancelled. Meanwhile the rest of RWBY and JNR went to Chris, another Wielder, to ask questions and even bring up the No Aura thing. Like Tsubasa, Chris shows no Aura. While the rest of the team doesn't think much of it this gets Pyrrha really worried and talks with Cinder. And now Cinder goes into the next stage of her plan....by telling her about the Maidens. She gives the truth that Ozpin reincarnates, but twists the story that HE created the Grimm and that The Maidens are meant to be his hitmen. She claims that she broke away from him and he took half her power as punishment and is lucky to be alive thanks to her team. Pyrrha buys ALL of this and forms an alliance with Cinder.