There have always been competing schools of thought about what equality means, just like most difficult political issues. I think it helps to think about desegregation in terms of a number of different factions with different interests, and in terms of how those factions’ goals could or couldn’t be met by different solutions.
You had the virulent racists, and their goals were simple. They wanted to enslave people, and if they couldn’t do that, they wanted to de facto enslave them without technically doing so, and if they couldn’t do that, they wanted the absolute bare minimum of rights afforded to them, and so on. Their priorities were based on a moral philosophy that said whites were superior, often by the hand of god.
Then you had a broad range of moderate positions, of people who maybe thought true equality was impossible or maybe thought it was not desirable, who favored some limited form of accommodation. Some were moderate because of their own racism, and some were moderate because of their dim expectations of society, like you hinted at. They didn’t trust the country to give them any more than that, so they were ready to jump at the chance to get what they could.
For (mostly northern) white abolitionists, separate but equal was an idea that was morally unacceptable, because–again like you said–the reason for the continued separation mostly had to do with continued racial hostility: the white people because they were racist towards the black people, and the black people because… white people were racist toward them. To concede that the separation was necessary would be to admit that, OK, yeah, we can never not be a racist society, because we aren’t willing to do it. That was something abolitionists actively fought against, the white ones because of a sense of moral obligation to right the wrong, and the black ones because, well, duh.
So the more radical activists pushed for absolute integration, because they believed that was the only route to equality. Any separation stamped black people with a “badge of inferiority.” That was the reasoning behind Brown v. Board of Education; that no matter how much effort you put into making facilities equal, black children would always be harmed just by the historical fact that being white meant you were a regular person, and being black meant you went to this other facility.
But then the less radical and maybe more pragmatically minded people pointed to the reality of the situation, which was that Brown didn’t actually make anything equal for almost anyone on the day it was decided. There were still decades of battles and hostility and continued bloodshed because a lot of society was willing to fight those battles rather than accept integration. Of course, if you’re like a 27 year old white lawyer from Boston, you have a very different perspective and something very different at stake in those battles than a 68 year old black person in Montgomery. A lot of people thought, well, that’s nice, but it will never happen in the real world, and it would be nice to be able to just be safe from violence and be allowed to send the kids to any decent school, while a lot of other people were ready to fight until it did happen in the real world. It fluctuated over time, as that moderate group grew more and less willing to demand more government intervention in the matter, desegregation efforts were taken more and less seriously, up to the present day. A lot of school districts just never really desegregated, or desegregated exactly to the point they were legally required to, and then became segregated again immediately once the government left them alone.