Members of the so-called “alt right” or “manosphere” actually bear very strong similarities to cult members - they become increasingly rigid in their beliefs, they have decreasing tolerance for ambiguity (everything starts to become either right or wrong, with no room for grey areas), they become increasingly preoccupied with “purity” of thought, their beliefs start to become the core of their personal identity, they accept the word of thought leaders without question or critical thinking, their relationships with family and friends deteriorate, and they often experience negative consequences at work or school as a direct result of their beliefs. 

Dealing with a friend or family member who has joined the alt-right is very different from dealing with a family member who is dabbling with the idea of voting Conservative for economic reasons, or dealing with a family member who erroneously believes that Game of Thrones isn’t very good. Reasoned discussion and laying out your point of view will not work here. The tactics that you need to use with him are actually the tactics used to deprogram cult members, which includes things like:

• Do not debate him. Never debate a cult member under any circumstances. It’s a complete waste of time for everybody involved, and it only serves to further entrench him in his toxic beliefs. Cult members do not approach debates in good faith - they are not open to having their minds changed, and they have no intention of ever listening to the other side. Cult members use debate as a tool to recruit people with possibly like-minded beliefs, or as a tool to gather evidence that the “other side” is delusional. The more you debate, the harder he will fight to come up with justifications for his beliefs, and the more satisfaction he will get from feeling like he is defending his “side” from attack. Shut down all debate with him. If he tries to start a debate, redirect immediately. If he makes an inflammatory statement at the dinner table, respond with something non-committal ( “hmmmmm”, “is that so?”, “okay” ) and immediately change the subject. Don’t get sucked in. No matter how hard he tries to open up a debate, deflect, shut him down, or walk away. 
• Treat him with detached politeness. I know that it is very difficult not to get visibly upset when someone is insulting the very core of who you are as a person and what you believe, but but you have to stay calm and detached here. Do not let him see that he is upsetting you. When he is going on rants about his beliefs, treat him like a child who is explaining the rules to a video game that you don’t particularly care about - have an air of detached boredom, and no matter how hostile he gets, respond only with politeness. Remember, part of the core beliefs he’s being fed is that people outside of the alt-right are “emotional”, and that his beliefs are “triggering” to those people. Give him no evidence to suggest that is true. Stonewall him. Give him nothing but bored stoicism in response to his outbursts. No matter how much he escalates or how horrifying his beliefs get, always act as though you are having a polite conversation about the weather with a stranger at Starbucks. If he tells you that women should should be property and gays should be killed, respond only with a polite “Well, I suppose that’s one perspective”, or “Yes, I believe you have mentioned this before”. Nothing takes the wind out of a cult member’s sails faster than being treated with calm politeness when they are expecting a fight.
• Do not insult him or the people who share his beliefs. The glue that holds cults together is a persecution complex. Cults absolutely thrive on being persecuted for their beliefs, and they depend on it to keep members from leaving. “People outside this group hate you and they will treat you much worse than we will” is the message that keeps people from leaving hateful cults, all the way up until the Kool-Aid is served. He is being fed the message by his fellow cult members that he is hated for who he is - a, presumably, straight white man - and that “Liberals” hate him so much that they want to take away the things he is “owed” (money, power, security, etc) and give it away to undeserving minorities who haven’t really “earned” it. Give him no evidence to suggest that this is true. Refrain from insulting him, or insulting the people he views as thought leaders or role models. You can definitely express your political opinions and make it clear that you are not buying into your brother’s worldview, but keep things direct and refrain from personal attacks. If he is gloating about the president to intentionally get a rise out of you, a simple “I disagree with his policies” is all you have to say - launching into attacks about the president’s looks, family, mannerisms or intelligence is fuel for your brother’s hateful beliefs. Remember that when it comes to your brother, you are not acting in the role of a left-wing activist facing off against a dangerous right-wing activist with a platform. You are a concerned family member dealing with a family member who has gotten involved in a cult. 
• Ask polite questions, but do not engage directly with his beliefs. Do not read any of the reading material he recommends, listen to any of the podcasts he puts forward or view any of the videos he asks you to watch; it might be tempting to do so just to prove that you are engaging with him in “good faith” and that you have given his views an “honest try”, but this is a mistake. There is no such thing as “good faith” or intellectual honesty when it comes to cults, and there is nothing to gain from engaging in their propaganda. Do not treat anything produced or recommended by a cult as if it has value, because it does not. When he provides you with something he wants to you read, behave as though a young child has just handed you a live earthworm - thank him for the gesture, but decline to accept. Engaging with propaganda just legitimizes it, and gives him more ammunition to hunker down in his beliefs. When you do ask questions of his beliefs, be detached and polite. If he is ranting that all women are whores, ask him what the basis is for that belief. You are not looking to debate him or get a rise out of him - don’t fire back with counter-points, but make a polite, disinterested noise of acknowledgement, or ask for further clarification. You are merely looking for holes in his reasoning, or gaps where he doesn’t have evidence to back up what he says. You don’t need to point these holes out to him - there will be many. When he is unable to be specific, once again, make a polite acknowledgement ( “Interesting.” ) and move on.
• Emphasize how much you miss your former relationship with him. Tell your brother that you miss him. Be specific - talk about the things that you used to do together, and the ways that he used to be involved in your life. If he tries to deflect and start talking about his beliefs again, or how he can’t be involved with you anymore because of your own beliefs or identity, don’t engage. Go back to talking about how you miss the relationship you used to have with him. If he insults you, pretend you didn’t hear him and remind him of a happy memory or a fun thing that you used to do together. It can take a really long time to have success with this tactic, but your brother does remember the relationship he used to have with you, and it is possible to remind him of what he is missing out on by continuing with his hateful beliefs. The idea is to take his beliefs out of the equation as much as possible - make him miss the relationship that he used to have. Any attempt at mending the relationship on his end will necessarily require that he get less extreme in his beliefs - it’s difficult to pursue a close relationship with someone and still insult them. 
• Remind him of normal life outside the cult. People in the alt-right - and other cults - tend to become hyper-focused only on issues that concern the cult, and begin to forget about normal life. Your brother is likely spending a lot of time and focus on things like the “sexual marketplace”, abortion rights, refugees, gay rights, female superhero movies etc. Bring him back to earth as often as you can with reminders of things that are outside the scope of the alt-right, and are minimally politically charged. Start a conversation about a new restaurant that is opening up in your town. Show him a funny cat video. Ask him if he’s seen a minimally controversial movie. Constant reminds of normalcy can gradually help him realize how hyper-focused he has become on a few small issues, and remind him that his worldview and priorities are incredibly skewed.
• Protect your own mental health. Living with a cult member is exhausting. The combination of fending off the insults, being bombarded with hate rhetoric and missing the person they used to be is exhausting. Make sure you are protecting your own mental health. Take breaks. Leave the house and spend time with other people. Lean on friends and other family members for support. Take care of yourself. Getting someone out of a cult is a marathon, not a sprint, and it’s important to conserve your energy. It can take up to five years to get someone to fully leave cult beliefs behind. Be patient. 

One of the hard parts about dealing with alt-right family members is that people make the mistake of approaching them as a political movement, when it is more appropriate to address them as a cult. The way that they operate is much more similar to the dynamics of a cult than the dynamics of a mainstream political movement, and deprogramming techniques are your best bet for getting your family member back. I highly recommend that you and your family read up on cults and the tactics used to get people out of them. It is especially helpful to read testimony from people who have escaped cults or successfully been persuaded to leave them - if possible, look for materials from people who have left the alt-right, and try to present this material to your brother. This is an incredibly difficult thing for a family to go through, and I highly recommend that you seek out other families who are dealing with similar situations - you are far from alone here. 

Best of luck to all of you.