We agree this does not have to be either-or. Socialists have always been at the front of the struggle against racism.
But we need to be clear about what's most important if we want to solve the problem of police killing. The police mostly kill poor people, and they kill them proportionally to the racial mix of poverty.
And no. class is not traditionally part of intersectionality, which is why it fits so badly. Intersectionality is about social identity—Crenshaw's first version was about race and gender. Economic class is about your relationship to capital.
Redlining was based on poor neighborhoods, not race. Yes, that meant it disproportionally affected poor black people. It affected poor white people too. Those neighborhoods were class targeted. Richer black people were not redlined.
There's a name for refusing to acknowledge that something almost exclusively affects the poor: race reductionism.
I have read the people you name. I favor people like Adolph Reed and Barbara Fields, as well as King and Malcolm X after he left NOI. I would especially recommend Racecraft to you.