How ridiculous it is for Matt Lewis of The Daily Beast to write, "It seems observably true that libertarianism is disproportionately a gateway drug to the alt-right."
To say the libertarian movement is a "gateway drug" is to say more than that some prominent members of the alt-right once called themselves libertarians. It's also to say that alt-rightism provides a purer form of what those members had found in libertarianism (aka original liberalism, or simply liberalism).
A good measure of ignorance of liberalism is required to entertain this thought. Libertarianism is a more formal version of (classical) liberalism, the social philosophy that blossomed in the 18th century but had roots in previous ages.
The liberal worldview was self-consciously universal, applicable to all people everywhere because all human beings had the same basic requirements for flourishing. Religion and culture mattered only because they might explain variations in the ways free people pursued the good life. But the basics were expected to be more or less the same because people are people, that is, "created" equal.
Liberalism has recognized the importance of respect for property to the quest for the good life. This is not difficult to fathom. How can one flourish in an environment in which one's possessions are subject to confiscation by the state or freelance marauders? This point is reinforced when one remembers that plans can extend over many months and years. Who would delay consumption a long period without reasonable certainty of being able to enjoy the fruits of one's labor and forbearance?
So, yes, private property is central to liberalism. But liberals have historically seen property as an institution engendering not exclusion, but inclusion. Free trade and the widest possible division of labor have been just as dear to liberals as property rights—the connection is obvious. You see this clearly in Adam Smith and Ludwig von Mises.
Mises in particular located the source of wider social living in the perceived potential for gains from trade and toleration. Liberals have seen the division of labor and free trade as indispensable to human flourishing, but those things cannot exist securely without mutual respect for every person's title to their own stuff. As an institution, property was of a piece with cosmopolitanism and exchange of all kinds. That's why a "pure" race or culture is as chimerical as a "pure" language.
Sure, property also authorizes owners to exclude from its use those they wish to exclude for whatever reason. But that hardly seems to have been the focus of liberals. Rather, property was about ever-greater opportunities for interaction—race, culture, and national borders notwithstanding.
The exclusionary side of property could explain why some individuals flirted with libertarianism before going on to circles of racial and religious bigotry. Perhaps those individuals were attracted to the exclusionary features of property but then got turned off when they saw the overriding lure of inclusion that property and trade present. So they moved on.
Another explanation is that some people are attracted to a "fringe" movement not because of anything particular to it but because like the idea of being a big fish in a small pond. If for some reason one pond doesn't suit, they may jump to another "fringier" pond.
No matter how hard one might try, it is impossible to twist libertarianism into something it is not. Property can be used to advance bigotry, but so can a printing press or a website. No one thinks this negative potential taints the ideas of free trade and free speech, which predominantly foster increased contact across former divides. Likewise, the wish of some to use property in the cause of bigotry does not detract from the institution's monumental contribution to peace and harmony among diverse people.
Maybe a few self-described libertarians cling to the idea that property is essentially about exclusion, but they are fated to hit a wall: liberalism is a spirit as well as a set of ideas, and it cannot be turned against itself. It fosters human solidarity, not separation.
Libertarianism, like its precursor, is an answer to the question: under what conditions do reasoning social animals best flourish? In answering that question the way it has, liberalism offers no home to sowers of division.
This not to say that a few participants in the libertarian movement haven't infamously pandered to alt-right types in search of donations and bodies for events. This has done the movement an injustice because it lets antagonists suggest some that substantive connection exists between liberalism and illiberalism.
Some libertarians have also encouraged the idea of a connection by their inept explanation of the libertarian position on public-accommodation and employment anti-discrimination laws. The libertarians I have in mind give only half the explanation when they insist that property owners have the right to exclude anyone they wish. That's true, but libertarianism properly conceived goes further in light of the considerations outlined here. The rest of the answer is that even nonviolent bigotry is illiberal because its collectivist premise clashes with the firmest grounding of the case for individual liberty and is thus properly a matter of concern to libertarians as libertarians. (See "What Social Animals Owe to Each Other" and "Libertarianism = Anti-Racism.")
Therefore, when libertarians are asked if bigoted property owners should be free to discriminate, they should say, "Free of government force, yes, but not necessarily free from costs imposed by consumers." In other words, bigotry should be fought without help from the state, where appropriate, through boycott, ostracism, and publicity.
Thus those who migrate from the libertarian movement to the alt-right have rejected the essence of the freedom movement and its philosophy. They are certainly not looking for a purer version of it.