There is no inherent reason you should care. I just do. It comes naturally. Maybe it’s a result of my moralist socialization, maybe you could chalk it up to some kind of empathy instilled in me as a child by my parents, I don’t know.
But I also care for my own reasons. I am bored, stressed, lonely, and spiritually dead due to a world which assigns me a function for the sake of capital (or order, or civilization, etc). In this way I am alienated from my own life, which means the life I live doesn’t feel like something I can grasp or get a hold of in any way. Meaningful relationships, an interesting life, the ability to control my own fate; all these things have been robbed from me due to the material conditions of the world. It doesn’t provide any adventure; it’s been shaped for the sake of those previously stated things (capital, etc). At best I can continue to experience such despair, at worst I can starve to death. So I identify the woes I experience as being symptomatic of a larger system (civilization, capitalism, whatever you call it). For these reasons I want to destroy the system. If other people also want to destroy the system, then I tend to feel solidarity or affinity towards them.
I care about these people and their struggles because I understand that capitalism only works if everyone plays along. If these extra exploited people revolt in some way, the conflict that such a revolt brings has potential to generalize and possibly destroy the system. There used to be a dominating narrative that these ‘more exploited’ people are inherently more likely to be the agents of bringing about this destruction of alienation and exploitation. I’m not so sure if that’s true. But for me it isn’t their position of extra exploitation that leads me to feel solidarity with them, but rather if they are hating/attacking the system.
edited for grammar corrections/clarification.
