Definitely. The prison system in especially California and Texas is an extremely segregated place. An organization like the Aryan Brotherhood was born out of the fact that unaffiliated white inmates needed strength in numbers to protect themselves from the much larger Black and Hispanic organizations that were already established.

Nevertheless, when you talk to people who have done time in for instance the California prison system, it also becomes clear that it's not always racial.
For instance, inmates that are members of outlaw motorcycle groups (who tend to have both white and Hispanic members) mostly hang out with each other instead of joining other prison gangs.
Within the Hispanic group you have the clear division between the Southerners controlled by the Mexican Mafia - which are mostly members of Mexican gangs from the Los Angeles area as well as members of Salvadoran gangs - and the Northerners controlled by the Nuestra Familia - which are mostly members of Mexican gangs from Northern California. However, for some reason members of a gang like Armenian Power (Armenians being not a Hispanic, but rather a more Middle Eastern looking ethnic group) also tend to stick with the Hispanic Southerners.
Within the African American group there is a ton of division. You have Crips and Bloods that all come from different rival sets. You have black inmates from the Bay Area that don't uphold any Crip or Blood colors. All of these groups don't necessarily stick together. Sure, you got the Black Guerrilla Family (which has a substantial following among inmates from the Bay Area) but they have not been as successful in governing all black inmates like the Aryan Brotherhood did for unaffiliated white inmates, like the Mexican Mafia did for Sureño inmates and like the Nuestra Familia did for Norteño inmates.
The you also have the "Others", which is just a catch-all name for Asian and Pacific Islander inmates that come from a variety of gangs - mostly Vietnamese, Chinese, Cambodian, Hmong, Korean and Samoan. In spite of the ethnic differences they also seem to somewhat band together.

Important to note is that ALL of these groups do politic together. Despite the clear segregation, "racial wars" are basically non-existent and the vast majority of the violence being done by prison gangs is the result of these organizations cleaning up their OWN yard. A "peckerwood" misbehaves? A white shot caller is gonna ask to take care of him. A member of a Norteño set misbehaves? A Nuestra Familia shot caller is gonna get him done.

There are also internal politics in check. A lot of the Los Angeles area black gangs also have a ton of members that actually have Belizean ancestry instead of US-Born African American ancestry: Rollin' 30's Crips, Rollin' 40's Crips, Black P Stones Jungles and Fruit Town Brims for instance are notorious for having a disproportionate amount of Belizean members. And despite these gangs all having rival sets, members of Belizean ancestry often politic to make sure they don't have to whack each other.

So I 100% agree that all of the prison groups, especially in California and Texas, are racial...but there are also a lot of nuances.