As long as we don't seek to understand why people act this way then it makes sense to not care.

Literally the reason you can't care about these people is because you can't see them as people. You see actions you would never commit and assume only some sort of non person is the only type of person that could commit this. They are like you but not. They are an "other".

Instead of looking at these actions as rational, see them for what they are. Mass rage. Ever been to a concert where a lot of people are enjoying the music? Or a giant comedy festival with a sea of laughing people? The mass emotion is palpable.

Rage is no different. Because of systemic and complex reasons if you have black skin in America things suck for you. Look at how often /r/all has something to remind you that certain people hate you for an increased level of pigmentation activity. It's absurd.

So if the narrative is black people are sub citizens which results in black people living sub citizen lives. This leads to frustration and irrational acts from that frustration. These acts are not responded to with the compassion and understanding they require to be understood. Instead the problem is re-enforced.

if you don't fucking care about your own community, then why the hell should I

They don't have any other choice. From where you are of course they do. But you aren't them. If there was some other avenue they had access to I garun-fucking-tee they would take it. But the likely issue is they face problems from systemic poverty and racism.

A very good example of this whole phenomenon done somewhere else is in Canada with the indigenous people. Irrational fucking hatred up here. It's a contentious issue dealing with ongoing racial conflicts. They have their uniqueness of course but at its core is an ongoing rift between subcultures, where one is relegated to poverty and blamed for it. And when they get so angry they riot about it, people tut tut and talk about how it's only further proof. And these conflicts also result in the death of unarmed racial groups. The Dudley George incident comes to mind.

Assuming rioters are well organized, rational groups is stupid. People are emotional, not logical. We can act with reason in certain conditions but absolutely can be pushed to extremes. Watching this behavior and assuming you know enough about the situation to judge their actions as foolish is nothing more than fundamental attribution error. Which feeds confirmation bias blinding you from the completely different angle you have to look at to understand why people act this way.

At the base of these issues isn't race. It's poor understanding of human bias.