I am a libertarian-authoritarian mix myself.
Basically, I believe the best government is a local authoritarian government, where variables are known, and the ruler is close to the population, for example Singapore.
When you go stupid-big sized countries (like US, Brazil, Russia...), you have a problem: these countries have too much land and populations to manage efficiently.
In those cases, the ideal solution would be a libertarian FEDERAL government, while local governments (municipalities and states) can do "whatever" they want as long it doesn't put national security in danger.
That said, there are some authoritarian rules, that if applied to the whole country, aren't 100% bad, they are not ideal, but it might work, for example avoiding war, encouraging reproduction (specially among the elites), protecting your economy from external threats, reducing the economy internal mess (subsidies specially are problematic), and so on.
I was curious about this, so I looked it up. From Thiel's writings on Cato Unbound:
> Since 1920, the vast increase in welfare beneficiaries and the extension of the franchise to women — two constituencies that are notoriously tough for libertarians — have rendered the notion of “capitalist democracy” into an oxymoron.
Later:
> It would be absurd to suggest that women’s votes will be taken away or that this would solve the political problems that vex us. While I don’t think any class of people should be disenfranchised, I have little hope that voting will make things better.
I'm not quite sure what he's trying to say. It sounds more like nonsense than any sort of actionable malice to me. (But then again, I don't really care about Thiel in the first place, so maybe I'm a little biased.)
Yeah, it's such a hassle trying to understand people who hold different opinions from yours. And reading their own words? Bor-ing! Better to just vaguely handwave some half-remembered boo-words you read in Vox and call it a day.