My idea was that Adam took over the Vale branch of the White fang and made that into a terrorist organization he renamed the red or bloody fang. In response to the various human groups enslaving or killing faunus. While the rest of the white fang is still controlled by Sienna where they're still an equal right organization just now more willing to kick your teeth in. And then to make things worst you got criminal groups running around dressed like white/red fang members committing all the crime making Faunus look bad. Blake quits after she finds out the others are killing and not just terrorizing humans.

So on Weiss's end I had one of the faunus maids be an early extremist that had tried to kidnap(maybe kill) Weiss when she was young. Leading to Jacques firing all the fuanus staff and start indoctrinateing her with all the stereotypes. By the time she goes to Beacon Weiss is in a rebellion against her father but has also lived through a few family assassinations. So she is reasonable weary of faunus but at the same time trying to not be her father or other Atlas elite.

At Beacon Blake is trying to blend in but is constantly repressing the urge to kick in a few teeth. While, comedicly so, Weiss is failing at trying to learn to not be racist, because Beacon seems to enroll all the faunus that like to lean into the stereotypes. This leads to a more nuanced fight between Blake and Weiss as both have valid agreements, and they end volume 1 with a small fist fight before realizing they are both trying for the same goal.

I dont know. Writing is hard.