I have an earlier answer, if you're interested! (It was in reference to photos, not videos.)

According to Jim Marshall, Cash's audience for his two January 1968 concerts included black, white, and Hispanic prisoners alike. And Marshall should know--he's the guy who took the photographs demonstrating exactly that!

Black Americans have been incarcerated at rate disproportionate to population demographics since--surprise, surprise--white people killed Reconstruction. This has been as true in California as anywhere else, and perhaps insidiously so given the state's generally liberal reputation. And Folsom Prison had its part to play. In 1940, California's population was 1.8% black but the population of inmates at San Quentin 9%; Folsom, recently reorganized into the state's maximum security prison, had a black population of 12%. As more and more black Americans sought safety and success in California over the decades of the Great Migration, the black prison population swelled. By 1960, black people comprised 5.6% of California's population and 22% of new prison inmates overall.

So what gives with the photo?

Like most prisons, Folsom had a long history of internally segregating prisoners where it could. And as testimony after testimony reflected, into the 1960s this was an explicitly and purposefully racist move. In 1943, a black man incarcerated at Folsom wrote to a committee sponsored by the governor:

Our servitude here is limited to inferior work. The only work that is given to Negroes is such as porter work, digging in the ground and breaking rock or what ever else the white inmates don’t want to do.

To be clear, Mills was only describing the few white men who were also forced to labor in the quarry alongside the black prisoners--most whites had better jobs altogether, including some that took them outside prison walls. (The quarry was later closed when outside groups and labor unions protested that it was taking their jobs). It's no wonder that black intellectuals like Angela Davis and Eldridge Cleaver (himself incarcerated at Folsom) depicted the American prison system as the new plantation slavery.

The situation wasn't any better either away from labor in Mills' day or during the 1950s and 60s, either. Black prisoners were routinely shunted to overcrowded cells on Folsom's top floors, suffering the worst in midsummer sweltering heat and always called last for recreation and meals. In 1959, a lawsuit brought against Folsom by a black inmate claimed that this was an ongoing problem, along with other officially imposed efforts at segregation.

Ethan Blue, meanwhile, highlights the de facto social segregation imposed by inmates on themselves even in common spaces:

There was plenty of [cross-racial collaboration and antagonism in the prison yard], when black, white, Asian, and Mexican prisoners gambled, traded, joked around, and even loved each other...Nevertheless, racial segregation became the norm in San Quentin and Folsom. White prisoners enforced racial spaces to delineate privilege and hierarchy...Black prisoners could be booed (or worse) if they tried to sit and eat in the “white” section of the dining hall.

Music, so racially politicized outside prison walls, became another focus for both crossing racial lines and policing them. Prison radio stations' variety shows happily broadcast performances by "in-house bands" like the (black) Hot Jivers and the (white) Rhythmic Stringsters, and individual performers might even cross racial lines to perform together. But when shows' hosts picked inmates to interview, they universally selected guests who "sounded white," and often used racially-coded descriptors like "freckled" and "ruddy" to affirm the audio's stereotypical assumption. And eagerly-anticipated drag shows and other annual events wouldn't be complete without a good dose of white prisoners in blackface.

So there were good reasons both for inmates of all races to attend Cash's concerts at Folsom in 1968, and for white inmates to try to muscle out black and Hispanic prisoners. Nevertheless, Johnny Cash was able and eager to close his shows with a song written by a white inmate, and shake hands with black and Hispanic inmates in the prison yard afterwards. But I mean--this is a man who prefaced a performance of Battle Hymn of the Republic ("As [Christ] died to make men holy / let us die to make men free") with remarks about how the song brought together a cleft country as soldiers and mothers on both sides could sing it. Whatever his own or prison racial politics, he at least wanted his music to bring people together.