It was a relatively new phase of the movement
which spanned the spectrum from Stokely Carmichael telling blacks to go back to Africa. Eldredge Cleaver the Algerian rapist who believed black liberation meant raping white women, Angela Davis, Black Panthers, George Jackson, Huey Newton, Rap Brown, or Black Muslims & Malcolm X into guns & Islam. All facing a very racist FBI Director J. Edgar Hoover using undercover informants and agent provocateurs.
Then more "moderate" MLK, and John Lewis, with Gandhi like pacifism, non-violent protests, and even traditional black conservatives who didn't like integration, opposing interracial marriage from a traditional black perspective.
Farmer's CORE, Congress on Racial Equality, more into jobs & economic issues, or Jewish Sammy Davis Junior who joined with Richard Nixon. Or Thurgood Marshall taking the legal court route to SCOTUS.
It was an era of women's liberation, gay liberation, the Vietnam War with major divisions everywhere, not "just" civil rights.
Then there were regiional geographic differences. religious differences, black church leaders vs. more secular, young vs. older activists, along with ideological, strategy differences.
like any movement or political party, there are various wings, disunity, conflicting personalities, different emphasis on issues, strategy and long vs. short run objectives
all guided indirectly by white Democrat or Republican politicians trying to promote political agendas siding, promoting one or another side with conventional propaganda and financial funding/bribes.
But even then, was it really that difficult to stay together? Does the quesiton have a false premise? Nothing brings people together more than having a perceived common enemy. The enemy of your enemy is your friend is the ancient maxim.
but even in pre Civil War days, Harriet Tubman and Fredrick Douglas disagreed over John Brown's raid on Harper's Ferry. Diagreements are very common. Rosa Parks was even disowned by her own NAACP who put her up to the bus segregation protest. She had to leave Alabama, go north to find more support.
but for a better answer to your question, look to those who can provide you with more personal experiences.