Thanks for the links.

I would guess, though, that the author of "White Fragility" at least thinks she's on the left, maybe even the radical left. And I don't think that book helped to reduce the divides we were talking about. (I still don't have any answers for what to actually do. What do you do with people who think they're with you, and who are both theoretically and practically against you? And who label themselves with your group?)

There is definitly a lot of cognitive dissonance amongst people such as the author of White Fragility. The best solution for them is figures such as Chris Hedges, Richard Wolff, Cornell West, and Bernie Sanders. I think ultimately the issue with this lies upon the media - the views of the left are constantly misrepresented, and leftists such as Chris Hedges are outright banned from the media - he was fired from the NYT for opposing the Iraq War. Ultimately what you have to do is to build local organizations, vote very heavily in local primaries to get people such as AOC elected, start unions. It's a very difficult fight. You'll notice too that people such as DiAngelo in the mainstream media will generally attack leftists on aesthetics and ignore their points, like what happened with Sanders.

Additionally, people politically have tried to label themselves as leftists (including the Nazis - they called themselves National Socialists as they were signing deals with Krupp to make unions illegal and preparing to execute members of the Socialist and Communist parties). When those people have hegemony, it's a difficult fight.

Ultimately I think the basic distinction between leftists and people that pretend to be leftists is always economic. If you get the platform, the best attack vector is to focus on how useless their ideology is to fix economic issues, and how these economic issues are the engine of racism. If you manage to get them to admit that their economic policies do nothing to help the poor and the common man, it becomes very easy to call them out as not a leftist. But getting that platform is exceedingly difficult, even when you're a professor in economics at MIT, a Pullitzer prize winning journalist, the most popular politician in the US (see : Bernie Blackout), or an acclaimed doctor in Philosophy and influential critic of Obama (such as Cornell West - if he was a Republican he'd get twenty times more airtime).