Very interesting article.
I believe in focus on the concept of "class" and "race" you would be much more effective if you focused on "culture".
"Culture" influences peoples views of how to interact, how policing should work, and what laws are valid. That's intuitively obvious.
Gays for example always stated that laws against sodomy and gay sex were invalid. More cultures now agree but not all. Gays also have their own culture on how to interact and what policing is relevant (e.g. the gay culture does not have the same issues with rape as str8 culture).
Its easy to see how culture affects peoples view of interaction, policing, and laws. Take Trump and MAGA supporters as an example. Trump has transcended the cultural signficance of whether a "grab em by the pussy" comment is inappropriate. Many also believe the judgement against by Carroll is also invalid. Many have no clue about what the judgement relating to Stormy is. Many don't believe what people did on jan 6 was any different than what happened in BLM marches. I double you can create a "class" or even "racial" story that makes broad sense for the MAGA movement. The only one that makes sense is that people are prioritizing cultural issues (e.g. abortion) over issues they view as now culturally insignificant - e.g. sexual immorality.
If the divided states continues to use race and sexuality as the group identification in the population, it will continue to miss the real point. The country is the most cultural diverse in the world. That cultural diversity stress any "system" that spans cultures. That's what clear happened in the George Floyd case. I doubt most of the Black people in Minneapolis viewed that George Floyd was a problem in the community. He was harmless and in many cases seemed to have been a positive force. He was breaking "laws" but not ones the Black community really cared about as far as I can tell.
The people who viewed him as a problem where not part of the Black community culture. The shop keeper thought he had a counterfeit $20 bill. Where would George Flyod with malice of forethought have acquired a counterfeit $20 bill? The shop keeper was Palestinian. An entirely different culture that likely viewed George Flyod was afflicted with common vices. Not to be trusted.
The bottom line, there is really no way to create a common solution that spans the divided states for problems in policing, schools, etc. Community and specifically communities with common culture are the best place to address these issues.