1. Some libertarians are sort of contrarian dilettantes, AKA nerds, that is, people who are attracted by offbeat ideas and can get all caught up in them. There's a little bit of that sort in me. The seem like nutcases to regular people who are interested in what people are supposed to be interested in, like sports or popular music. And, well, some of course are nutcases, but don't have to be. Just a little eccentric. Take me for example. I've been into Esperanto and other artificial languages, even developing my own [link], And I've always been a science-fiction reader — and that's a nerdy bunch. It doesn't necessarily include people who watch SF movies, but does include most readers.
2. Another group is basically liberals, often social justice warriors (SJW's), who may have a touch of contrariness like #1, which leads them to be basic, standard liberals, except that they have a better understanding of things like economics and the Second Amendment, which modifies their liberalism and leads them to consider themselves libertarians. That's the faction I'm always trying to straighten out, because I think they do more harm than good.
3. This is what I basically am. The standard American type, who considers the Founding Fathers the golden standard of freedom. We're libertarians because we consider personal freedom both very desirable in itself, and also a prerequisite for a progressing (not to be confused with "progressive" — See #2) society. We think in terms of establishing a political system and climate that effectuates self-sustaining liberty, which is why, unlike the #2's, we tend to discourage dysfunctional behavior, like weird sex, drug addiction, and other forms of degeneracy. We know damn well that a free society has to be sustained and defended, so we're in favor of a strong military and a stringent standard for immigration, only allowing immigrants who can and will help sustain and defend our system. Hint: This mainly won't include Somalis or Syrian "refugees." Like I say, that's me, with a touch of #1.
Finally, as Matt says in the quibcag, many libertarians, mostly that #3 bunch, but the others are welcome to take the red pill and help out, are leaning towards the alt-right position [link], which is that we can't just go around being libertarian and ignoring non-libertarians, but that we have to be proactive about it, and vigorously oppose those who would overwhelm us with their PC authoritarianism and globalism. And if this takes a little rough stuff, so be it. Lord knows the enemy is glad to bloody some noses.
Quibcag: The swordgirl is Ranma-Chan of Ranma ½ (らんま½)