Well, I don't see why no progress would be made in the South through the 1950s and 1960s if they start the same as IOTL. Is the Warren Court not going to overturn Brown vs Board of Education (it was unanimous after all)? Is Eisenhower not going to send Federal troops to enforce the decision in Arkansas?
The Warren Court will likely overturn Brown v. Board of Education, but there's nothing saying that Eisenhower will send troops to enforce it. Or that Eisenhower has to be President in an ATL scenario-what if Bob Taft is elected and then dies, and then his VP decides to back down on the issue?
What about the other decisions of the federal courts? Is no black baseball player going to break the color barrier and join the major ranks despite several owners who finally planned to? Are southern blacks not going to organize and demand changes?
What if they organize and demand changes, but fail? No symbolic Civil Rights Act in 1957, no successful Montgomery bus boycott? This could possibly discredit non-violence as a means of gaining ground; there were those who turned their backs on it in OTL even with rapid gains.
And Jackie Robinson was a symbol. An important, relevant symbol, but without any accompanying progress it does him no good.
Witht he US engaged in a struggle against world Communism, are the country's elites going to simply allow all moral authority to ebb away? There is a very broad based change in society by then versus what the US was like, say, in the 1890s-1920s when attempts at civil rights could very often be met with violence and government approval of such.
But inertia remains a powerful force. Its not a certain thing that Federal troops will desegregate the Little Rock Schools; a different president than Eisenhower could play it more cautiously. Its not a certain thing that the Montgomery Bus Boycott will succeed, and that would go a long way to harming the idea of a nonviolent protest movement.
Too much had changed int he country by the 1950s and 1960s that civil rights progress won't be made. For no progress to be made, you need a very different 1950s and 1960s, which means an earlier POD. You need a 1950s which allows whites to respond with violence, the states to encourage it, and the federal government to do nothing. That combination does not exist IOTL. You can change individual events, but I think there will be others to replace them.
Why is Civil Rights progress guaranteed? Even in 1964, LBJ had to call in every trick he'd learned in the Senate to get the Civil Rights bill passed; JFK failed utterly to do it. It took maybe the best parliamentarian in American history, wielding the legacy of a martyr, to pass a major civil rights bill, and this is 14 years after 1950.
If you can find a way to make the Montgomery Bus Boycott fail, that could possibly discredit Martin Luther King. You do that, you open the way for more violent forms of protest in the South; it wouldn't start with bombings but with riots. All of a sudden, you've given "classy" segregationists like Richard Russell the opportunity to say with credibility that these aren't innocent victims but communist agitators. A few years of that kind of frustration, and then the first bomb goes off.
If you were to look at Northern Ireland in the mid-1960's, the idea that by 1972 there would be paramilitaries killing each other in the streets and bombs ripping pubs apart would seem insane, but any civil rights movement of that kind is walking a real tightrope, and it can go to hell in a handbasket very, very quickly.