does division creates hate?

Hi,

There is a problem that I notice in my society, and I'm wondering if there is any category in Psychology or Sociology that I can trace it back to. My society is too religious and used to follow tow of whom they consider the greatest holy men ever. These two were fighting each other in terms of ideas and beliefs and power, but they both passed away long time age. The thing is their followers, although from the same religion and sect and live in the same city, are still fighting. They want to keep their idol's heritage existing. So whatever a group makes in the society, the other does the same. For example, they both have their own charity organization, own school that teaches children in a way similar to their holy man values and ideas, etc. I was raised among that environment, and saw many fights among these two groups, but they never declare their agony to each other on public. And when I was a kid, I realized I don't feel comfortable being with the kids belonging to the other group although I had no idea about the history or the reason why there was two groups from the first place. Now, I have a goal to prevent parents from sending their children to such schools since it turns kids into tools of a stupid ideology and hate as they grow up. The problem is that these schools claim to teach children religion and values, not hate or history personal fights. That's true, but eventually "hate" is what taught through the unexplained existence of two identical types of groups that kids been thrown into. I couldn't find a name for such hate since sectarianism does not fit with this case.
However, is there any Sociological theory or evidence supports that "hate" arises among kids from merely separation or distinguishing differences?
I found some "Ingroups and outgroups" explanations such us the realistic group conflict theory, the Symbolic threat theory, the Integrated-threat theory, and the 7-stage hate model.
But not sure if these theories are related or if it's specific because it's not my speciality.
would you help me pease with this?