I've been looking more into the Civil Rights era within US history and it always struck me as odd that there seems little if any mention of Blacks being opposed to racial integration of schools and businesses. Was the opposition by Black communities just virtually nonexistent? If it did exist in a significant amount, why were they opposed to integration?
Odds are that if you asked a bunch of random adults who attended American schools to describe Rosa Parks, it's likely most of those who recognize her name will say she was a tired seamstress who refused to move when a white man wanted her seat. A few might know the more complex, accurate history: Rosa Parks was lifelong activist who made the strategic decision to not change seats on that day, with that bus driver. She worked with and for the NAACP and crafted numerous policies and actions. She was fierce, intelligent, and committed to Black liberation.
The term "Americana" is used to describe the collection of ideas, events, and people that are shared as a way to shape the country's identity. In effect, it presents America as a vast expansive country, built on big sweeping ideas crafted by larger than life men. Americana is about telling the biggest but simplest story we can about who we are. Thanksgiving is about the time pilgrims and Indians worked together. George Washington couldn't lie. Martin Luther King, Jr. had a dream. Rosa was tired. The hard work of history, though, and what you get at in your question, is about who the story is for and who is positioned as the hero in the story. We can see that tension play out right now as various groups prepare to celebrate the 100th anniversary of the 19th Amendment. While it's true women got the right vote in 1920, it only applied to white women. Black women wouldn't be fully enfranchised until the passage of the Civil Rights Act in 1964. We often see little mention of these details side by side because of the pull of Americana, which is very much centered on the experiences of white settlers, colonizers, and citizens.
Americana even impacts how we talk about the integration of schools - and why we don't often see mention of Black Americans who were resistant to integration - in American history instruction and pop culture. The simplified history allows white Americans to remain the heroes who fixed the wrongs that were segregation. (It also allows for the erasure of those who did the segregation. It's why we're more likely to know the name of the Black girl holding the books in this picture and not the older white women glowering at her.) Given that most American teachers are white women, it's an easier history to teach and it takes a lot of work to teach more complicated histories in school. (I get into the history of why well-meaning white teachers are more likely to teach a simplified - or wrong - version of history here.) In effect, resistance to integration doesn't fit with Americana. After all, why would Black people not want to be around white Americans? Why would they possibly want to keep their children away from white children?
All of which is to say, we tend to simplify the history of school integration to a single narrative about Black parents wanting to send their children to school with white children. The history that's often left out is the reason - money. Schools designated as Black schools were woefully under resourced when compared to those attended by white children. The buildings were often physically unsafe, with limited facilities and resources. As indoor plumbing spread across the country, schools moved bathrooms indoors. Black schools, though, trailed behind physical upgrades by decades. In contrast, schools built for white students during the WPA were sprawling testaments to public education with beautiful architecture, open-air courtyards, gymnasiums, and theaters. To be sure, it wasn't the same everywhere in the country, but it was common in regions where redlining made the split between attendance zones for white and black schools clear and those that mandated segregated schools. And there were likely Black parents who wanted to send their children to school with white children. But overwhelmingly, the advocacy behind school integration was in getting Black children the same resources white children had.
Which leads us to the answer to your question: Yes. There were Black parents who resisted integration. The arguments against generally centered on two things. First, the general acknowledgment among Black parents and educators that white teachers weren't particularly fond of Black children. That concern played out when immediately following Brown v. Board in 1954, entire school districts shut down, rather than integrate. One of the reasons cited for the closure was white teachers unwillingness to teach Black children.
Second, there were several leading Black thinkers and advocates who pushed for a full implementation of the concept known as "separate but equal" made familiar via Plessy v. Ferguson. Their argument was that rather than go to where the money was, they should push to bring money to where the Black children were. There was evidence this type of structure could work. In the early 1900's, Washington D.C. funded white and Black high schools at the same rate, resulting in high schools with barely any gaps in performance and graduation rates. When there was a gap, it was because one of the Black High Schools, then known as Dunbar, outperformed the white schools. Part of this was the fact the principal was able to recruit some of the sharpest minds in the country to teach as there was an entire pool of untapped thinkers unable to get jobs in their fields. (A bit more on that here.)
Historians who talk about the integration of American schools in the the 1950's and 60's will often talk about "massive resistance" as a way to help frame the scope and scale of efforts. Black parents and advocates across the country used every tool at their disposal to get their children access to a quality education. In some areas, especially urban ones, this resulted in groups working at cross purposes or seemingly in conflict. Leaders of the NAACP, the organization that shepherded court cases, advocated for a more strategic and unified approach to education and as such, those who pushed against integration for the reasons mentioned above, plus others, lost to those who advocate for it. In effect, the pragmatic leaders of the NAACP made the call that it would be easier to win access to the existing white school districts on a national level than it would be to fight for equally-funded, con-existing districts at a local level. As such, their resources shifted in that direction. The Black students who tested integration were given emotional support and training to deal with the white adults and students who didn't want them there. If it was possible, their parents were given financial support when they experienced hardship as a result of sending their child to a white school. Finally, they looked for places where there was overwhelming evidence "separate but equal" wasn't happening.
Ironically, I've simplified a complicated history for the sake of this post. But it's fair to say the history of Black activism is rich, inspiring, and full of diverse thinkers, theories, and ideas and unfortunately, much of that history has been simplified to a single narrative.
The single best book on this matter is probably "A More Beautiful and Terrible History: The Uses and Misuses of Civil Rights History" by Jeanne Theoharis. It's a remarkable book.