It's basically paranoia.
I know that, based on my involvement with deep politics research, I must be a 'crazy conspiracy theorist' and I shouldn't be allowed to talk about this, but there's quite a difference between 'the government is spying on people and has major roles in terrorism' and 'everyone who looks different from me or has a suspiciously Ashkenazi-sounding name is part of a conspiracy to destroy my gene pool'.
Remember when Trump retweeted that image macro from 'WhiteGenocideTM', based in 'Jewmerica'? Believe it or not, the alt-right actually thinks that non-white immigration combined with female promiscuity is a Jewish plot to destroy the 'white race' through outbreeding and crossbreeding. These are a few of the alt-right's obsessions: white identitarianism, immigration, miscegenation, promiscuity, and Jews.
The alt-right gets its origin in two primary sources: the white nationalist wing of the paleoconservative movement and the neoreactionary movement.
The first believes itself to be the legitimate successor to the Old Right from before World War II, in contrast to the moderate social conservatism, economic cronyism, and vehemently anti-communist foreign policy that defines mainstream conservatism. Some parts of paleoconservatism also go beyond the fetishism for Western civilisation to argue that such a civilisation is only possible for the white European gene pool. This is why many alt-rightists have an obsession with crime statistics and intelligence studies, as well as 'debunking' environmental determinism and other (better) explanations. (If you're interested in refuting these claims yourself, try Francisco Gil-White's magnificent online book Resurrecting Racism
Neoreaction, on the other hand, believes itself to go beyond conservatism altogether; rather than wanting to return to limited Constitutional government (or the paleoconservative interpretation of such), they want to replace it altogether with monarchy, technocracy, or some other odd scheme. HBD (human biodiversity; essentially repackaged eugenics) and whatnot also play a major role in this ideology, but the main focus is on reviving archaic forms of authoritarianism.
It's also important to note that many alt-rightists transitioned to the alt-right from anarcho-capitalism, a form of libertarianism that holds that the most logical interpretation of the non-aggression principle (N.A.P.) implies anarchy. Most anarcho-capitalists are not socially reactionary, though Murray Rothbard converted to right-wing populism and racism in his last years and Hans-Hermann Hoppe has certainly done quite a bit to push some anarcho-capitalists in such a direction with his extreme anti-immigration beliefs and support for the 'physical removal' of perceived 'degenerates' from society.
The belief in Western civilisation is at the core of the alt-right; the belief in aristocracy is at the core of neoreaction. What is at the core of the alt-right?
The rejection of equality in all its forms.
One of the reasons many traditional conservatives, including secular conservatives, are pro-life is the foundational belief in the dignity of human life. To the conservative mind, hierarchies exist for the benefit of all involved; those at the top use their power to help those at the bottom and those at the bottom work in exchange. Alt-rightists do not share this view, and believe that those at the top are not obliged to do anything for those at the bottom. Wagner's words ring true for the alt-right: 'History proves that man is a beast of prey. The beast of prey conquers countries, founds great realms by subjugation of the other subjugators, forms states and organizes civilizations in order to enjoy his booty in peace…Attack and defence, suffering and struggle, victory and defeat, domination and servitude, all sealed with blood; this is the entire history of the human race…'
It is their rejection of this ideal which allows the alt-right to claim that people such as Ted Cruz are leftists or 'cuckservatives'. While to a moderate conservative or liberal eye Cruz appears to be very far to the right with his theocratic mandates and love of crony capitalism, the alt-right can dismiss him as in bed with the left simply because he believes in the concept of equality before the law.
In order to agree with the alt-right, you must believe that your ethnicity is going extinct, that you are opposed on all sides by people that hate you, and that everyone who isn't at least a civic nationalist is aiding and abetting your demise. Black people that you run into? They want to kill you and take everything you have.
Mexican guys walking down the street? They're coming for your wife and kids.
Two gay guys kissing? Degenerates polluting your mind and the minds of everyone around them.
An Asian man and his white girlfriend? A race traitor providing evidence that whites are dying out.
Your nice Jewish doctor? Member of an elite ethnicity trying to take over the world.
This sounds insane. That's because it is. Doesn't preclude the alt-right from believing it.
I've talked to people who believe in shapeshifting reptilians who are not as paranoid or crazy as alt-rightists. Most people willing to believe in shapeshifting reptilians are also willing to admit they may be wrong; this is not true of the alt-right, who buy into racialist pseudoscience entirely. Worse, they tend to be rather skilled in rhetoric, so that when an unsuspecting person reacts to their racism by saying 'What the fuck are you talking about, you fucking racist?' they can use infographs and rhetoric to make it look like they're fact-based and rational when the data they're using is wildly inaccurate and subject to misinterpretation.
To the alt-right, it's a scary, dark world outside of their basements. Everyone is plotting against them. Every look at a woman, a black person, a trans person confirms this to them. Their idea of the 'red pill' precludes them from changing their beliefs until they take a long, hard look at them.
Of course, the real red pill is being able to change your beliefs based on new evidence and not shoehorn the evidence into your ideology.