So I'm sure that I don't carry any clout around these parts, but I feel a need to weigh in on this whole topic.
I'm noticing a lot of kind of permanent or totally unhelpful type responses to this issue (i.e. cut him off, just don't talk about it), but the reality is that neither is going to fix any of the inherent problems. Keeping quiet and avoiding the topic is not only going to cause OP a huge amount of psychic discomfort, but also does nothing to actually educate his brother. Likewise with cutting him off.
Look, I'm white. My wife is black. Prior to meeting her, I'd heard a lot of stupid bullshit about how people shouldn't marry outside of their race, about the difficulty of being a mixed race child, etc. I've had family from the south, supposedly, who were in the KKK. I fell in love with this woman, and I wanted to be with her, but I had what in retrospect is an insane amount of anxiety over how to approach the matter with my family. What would they say? Would they disapprove? If they did, what kind of decisions would I have to make? Who would I resent? All of that was eating me alive.
All of that turned out to be a non-issue. My family loves this woman, and they treat her like true family, and she loves them as well. Their racism wasn't some inherent flaw, but a result of several layers of ignorance and indoctrination, and the thing that helped to chip away at that was having a member of "the other" brought into their family. There was no pain to the process. They just accept things as they are.
Do they still hold some ignorant thoughts? Definitely. No question. But this is progress.
OP, it's not as though your brother possesses some genetic defect that makes him think and say racist things. You'd likely have the same inclinations. His problem is that he's a human being, he's young, he lives in an grotesquely confusing and tumultuous time, and he's managed to internalize some really harmful bullshit. He's likely regurgitating, at least on some level, shit that he's heard from other ignorant, indoctrinated people.
Without question, his thinking is harmful, it leads to hatred and violence, and there is no place for it in the world many of us want to inhabit.
You have several choices in front of you, all of which are easy in some ways and difficult in others but many of which hold absolutely zero value in terms of fixing the problem.
First, you can avoid the matter altogether by steering the conversation away from matters of race, politics, etc., and focus instead on pleasantries and distracting media- or sports- type discussions and move on with your life knowing that you're lying to yourself and to your brother.
Or
You can stop talking to him altogether, which is actually much simpler in the sense that you'll have to put even less effort into avoiding his rhetoric. You'll have removed one of millions of painful elements from your life, taking away but a single reminder of the racist society we live in, but you will have alienated your brother, possibly other members of your family, and you will have squandered an opportunity to actually help him change in some meaningful way.
Or
You can scream at him, which would be pleasant in some ways in the short term, and which may make you feel like a big tough person who took a stand and fought against racism, but what do you gain? A momentary satisfaction that you fought. But will your brother change? He'll know you're angry. He may avoid saying things that upset you to keep the peace. But will you have changed his mind? Likely not.
Or you can do the difficult, thankless work of treating him with the same love and empathy with which you'd ask him to treat others, and work with him in ways that may be slow going and imperceptible but may eventually bear fruit. It means being patient, understanding that while his ideas may be evil, he's still just a person. That the things he thinks, stupid though they may be, are a result of something (likely a fear or a frustration), and work to help him understand.
What really sucks about this is that there is no ease to this method. It's unreasonable to expect him to do the work, although we'd all like to. That's hard to hear, but it is what it is. He has no incentive to change his world view, and since his ideas are so primitive and baseless and irrational and hateful, he doesn't have to bring any facts or logic to bear in defending them. That's what I mean--his effort only involves thinking what he thinks.
Your effort will have to involve a good deal of self-education, patience, empathy, and constantly finding creative new ways to talk about why his thinking is wrong in ways that don't alienate him.
That doesn't mean you have to be tolerant of racism. I think that's an easy take away from talking like this, but that isn't the intent at all. But the practical reality is this: refusing to speak to these people or attacking them with anger isn't going to fix the problem. That's a totally unskilled and embarrassing way to deal with the matter. And I'm not saying don't be angry. Be angry. I'm angry all the time about this shit. But losing control of that anger and aiming at someone instead of conducting yourself with grace and dignity gains you absolutely nothing.
There are a lot of angry people on this forum. I don't begrudge them that anger at all. Again, lord knows I have my own fair share of it. But I'm so tired of seeing people fuck up over and over and over again by responding to people like your brother with even more mindless, stupid, clumsy anger.
Love your brother, OP. Be patient with him. But also teach him, and never back down on what you believe. Sacrifice in the name of a cause sometimes means sacrificing your own sense of self righteousness. You can do both of those things, and you can do them without fracturing your family. I live in Appalachia, and I am surrounded by Trump supporters and Blue Lives Matter types, and it tears me up inside. But I've made way more progress with these people by being patient and having actual mature discussion with them than I have by flipping out every time I hear something that insults my personal worldview. I haven't completely changed anyone, but I've made more meaningful progress than I would have if I had just gotten angry and walked away from the conversation because it was too difficult to engage.
At the same time, the fuck do I know?