I think another reason why RWBY's racism subplot just doesn't work is because of how much Weiss' story just pushes Blake's out the way. Weiss' racially loaded behavior is overshadowed because of her past with how the white fang influenced her father's behavior toward her--
which means that the argument they have in Volume 1 is placed on Blake because the story needs you to see the White Fang as this fanatical cult instead of a tragic result of Remnant's complacency involving the mistreatment of Faunus. So the Volume 1 finale is just Blake regaining Weiss' trust instead of addressing Weiss' engrained behavior from the results of her father's bigotry. And then Volume 2, they treat Blake's insistence on investigating why the White Fang is cooperating with an unapologetic thieving racist as a 'Blake' thing.
And then they just all wrap it up and turn it into 'Oh, its because of Adam, its all Adam--' without even talking about the SDC brand or diving into Sienna Khan and Ghira's history and respective outlooks or even talking about why Adam turned out the way he was.--
all to spend Volumes 7 and 8 focusing on how Winter and Weiss feels about the SDC and how it affected their family, and not the fact that Blake is literally placed in the middle of the most systemically racist place of them all that are very well responsible for most of what happened in her life. But nah, Blake's just cool with it, it was all Adam remember? Her parents back home got all that white fang stuff, it's whatever.
There's a more eloquent to write all this, but I can't bring myself to 100% like Weiss because they make it abundantly clear she's the band-aid to CRWBY's ill-attempt at a topic they were never equipped to talk about.