I read that TL years ago and for a time corresponded with rvbomally a fair bit. If memory serves, the chain of logic is not "black people getting rights -> space dystopia."
Rather his emphasis is on the fact that in order to achieve radical reconstruction the US government must use the Army to a much greater extent than it did in OTL. This leads to the military having a much larger role in American politics, eventually becoming something akin to a Latin American military junta. It is this much more authoritarian country that becomes a world power by that universe’s version of the Cold War.
I’m certain the more knowledgeable could poke holes in that logic, and there’s a fair argument that it’s problematic, but I never got the impression it was a deliberately racist screed.