It would probably require the USA to become properly speaking fascist. That would take care of the whole media issue--the point of fascism is to gain total control precisely because the working classes are becoming desperate and emboldened and cannot be allowed to communicate or congregate freely or they would take over. The thing is, it is the end game for a capitalist society; the normal functioning of capitalism in its competitive aspects requires liberal freedoms as do the free motion of the work force. Empowering some clique to override private decision making is to hand them the power to ruin the economy with a short-sighted kleptocracy; only if the regime is focused on some goal that imposes some form of reality principle on the kleptocrats that disciplines them to keep their eye on the economic ball can it keep from slipping into decay that long run benefits no one. So--liberal societies do not succumb to fascist rule on a whim. If there are more liberal options open, they take them.
So, engineering a USA that takes the steps necessary to suppress Civil Rights progress must involve the USA failing to enjoy the opportunities open to it OTL after WWII. In general the postwar period proved to be a buoyant boom period for all Western first world nations, as well as an era of optimism about the nominal political liberation of most of the world from formal colonial systems. Focus on the threat perceived from the Soviet bloc only helped facilitate the boom, so thoroughgoing fascist measures were not necessary--a certain amount of repression and ideological doublethink did prevail to be sure, but not to the extent that people who had the will to question were not left free to do so, albeit paying prices for it.
I don't believe making the war more devastating would change the basic circumstances. More people might die, the victory might have much more bitterness, but the survivors will enjoy the same opportunities; to create mass death on a scale where the shortage of people bites hard would probably be ASB.
Perhaps the best way to this kind of dystopia would be if there were no Second World War at all. In my hoary hobbyhorse view, Hitler was an example of an irreplacable man, perhaps and as such, he alone enabled the Reich to form and alone threatened Europe with war again; perhaps, without him, the various reactionary forces he was able to unite would flail about in mutual suspicion and while tending to dominate an illiberal and authoritarian state of Emergency Weimar, could not take that essential Fascist final step of crushing all opposition and silencing and hogtying the working class--so the vague threat of Red revolution is not checked in Germany, though it is not ever actually triggered either. Europe muddles through the Depression; Stalin the Great Procrastinator sits balefully on the sidelines, never calculating the correlation of forces favors conquest, not when that means empowering some generals who could turn on him anyway! Eventually he dies and the Soviets, unscathed by the Great Patriotic War, fumble about looking for ways to relax their overwound regime. Maybe they do better than OTL and hit on paths allowing for a deepening civil society that slowly normalizes the day to day appearance of Soviet society, even as it remains uncapitalist and develops successful models for planned socialism. Others might prefer to imagine it rather drifts back to a kind of state capitalism reminiscent of China, but with enough Communist ideology remaining to guarantee the workforces are getting a big share of the profits although others get much richer. No jumping out of upper story windows to get out of what amounts to 16 hours a day slave labor!
Meanwhile Europe has gone largely authoritarian on the German/Italian model; without Hitler to tighten the screws the reputation of Italian Fascism does not acquire the level of horror it did OTL--Leftists still despise it to be sure. Gradually Italy either succumbs to the kleptocratic rot, or else in weird parallel with Russia elements of civil society seep back in setting norms and standards and gradually lubricating and inspiring the machinery to work more competitively but also more effectively, with the on-paper still corporatist Fascist regime committed to raising standards for the workers lest they lose legitimacy completely. Britain and France, Western Europe in general including Scandinavia muddle along with liberal democracy and leftist parties, their reputations clouded by association real or attributed to the Soviet menace, still manage to win some elections and get some elements of social democratic policy enacted. Meanwhile the colonies are restive--the Japanese expansion of OTL 1941 never happens because they realize they face the American, British and French navies undistracted by war in Europe--I don't know if Japan implodes, manages to impose a terrible order on China, or softens up somehow, but they cannot go on a conquering rampage in the Pacific.
This leaves the USA with no one to war against, barring the prospects of brushfire wars in Central America--Mexico will offer no excuses to anger El Norte, though they might come close. Without WWII the US economy recovers slowly, and finds most of the markets of the world sewn up against it by European colonial systems or informal domination of places like South America. The Americans want opportunity somewhere but under liberal institutions there is no mandate for war. Indeed the most likely fascist types to take over are people like Douglas MacArthur, Charles Lindbergh, Henry Ford--a mixed bag of imperialists and America Firster isolationists, someone would have to escalate to Iron Heel levels of fanatical control before the country could be turned to war.
Perhaps the European powers would seem weak by the mid50s, having difficulty getting public support for the continuation of colonial imperialism, and spread thin. Perhaps it would appear that they are weakened by creeping Communism, if after Stalin's death the Soviet system appears more and more creditable. If the Americans are foolish enough to strike directly at British or French interests though I think the European powers would find a second wind, and perhaps would even formally ally with the USSR. Conceivably, when faced with serious and stiff resistance, American opportunists would quail and seek a truce, and double down on domestic repression while putting out some desperate propaganda story that no one really believes.
Even then, it is not inconceivable though definitely a bit risky and low probability that some American dictator might actually appeal to African Americans, might offer them, perhaps on an ad hoc individual basis, protection and status in return for service, and the path of American race relations might take a very strange turn indeed. There is as much potential for dystopian nightmare in that direction as there is hope, so I won't pursue it, I am just trying to indicate that the task of keeping Jim Crow going on a level without either worsening it or making it better is not so easy. More likely, if white Americans are also chafing under repression and manipulation in the face of slim economic pickings, that a volatile underground counterculture develops, which poses a visible and real threat for fascists to organize against; the demonization of African Americans does seem likely to worsen and with it perhaps mass genocide.
Maybe these tendencies are in a crazed sort of balance, and African Americans are not generally subjected to actual Holocaust, but are living in great fear and uncertainty and subject to new levels of arbitrary violence, both state sanctioned and wildcat. Gradually as the frustrated regime succumbs to corruption, greed, general inefficiency due to cronyism, some sort of revolutionary insurgency, perhaps hardline Communist, perhaps some more populist sort of authoritarian, perhaps with strong elements of genuine democracy, flares up, the nation churns through really destructive civil war, and some post-dictatorship coalition rules over the ashes and perhaps the coalition includes contingents of African-American freedom fighters, and their influence is heeded and racist rules are formally abolished. I would expect such an America to be semi-balkanized by the struggle--union prevails but regions have various local power structures, so in some white supremacists continue to rule but surviving African-Americans vote with their feet; in others black militias share power or even rule outright, and to a degree perhaps the racial tables are turned--again most whites fearing these places will be able to get out; in still other places a cosmopolitan rough equality holds.
I think the possibility the fascist regime goes full on Shoah instead is too realistic for me to face squarely; I'd rather just allude to it darkly and shudder at the evil and loss this would mean; such an America would be despised, but perhaps not shut out of the world anyway. I'll let someone else work that out if anyone has the stomach for it.
Simply muddling along with the level of repression of African Americans holding at roughly 1930s levels until the '70s or later suggests to me that a strongly fascist US regime, in the sense of being able to silence movements communicating the African American struggle, must have nevertheless fallen on depressing days of general stagnation and failure; the authorities are strong enough to dampen out repetition of dissenting language and prevent organization against themselves from gaining strength, but are just limping along day to day in a broken system. Such a regime of stagnant failure might appeal to yet another kind of artist to depict in detail. The thing about it is that while special levels of evil would be reserved for people of color, the lot of white people would not be a lot better. I am thinking of this as Francoist America. I suppose the odds of such a shambling ruin of a great republic ever recovering depend on whether the rest of the world achieves prosperity enough to provide opportunity enough for a post-dictatorship reformation to start recovering basic democratic values and a gradual improvement in the depressed standard of living; just maybe, again if African Americans play a major role in breaking the last rusty chains, racial equality might emerge along with gradual flushing off of the hangover of inefficient fascism.