He wrote an essay for Cato a few years ago that spells out his views fairly specifically:
http://www.cato-unbound.org/2009/04/13/peter-thiel/education...
There are some stark quotes, "I no longer believe that freedom and democracy are compatible" or "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.
In that sense, his support for Trump makes more sense.
In the face of these realities, one would despair if one limited one’s horizon to the world of politics. I do not despair because I no longer believe that politics encompasses all possible futures of our world. In our time, the great task for libertarians is to find an escape from politics in all its forms — from the totalitarian and fundamentalist catastrophes to the unthinking demos that guides so-called “social democracy.”
The critical question then becomes one of means, of how to escape not via politics but beyond it. Because there are no truly free places left in our world, I suspect that the mode for escape must involve some sort of new and hitherto untried process that leads us to some undiscovered country; and for this reason I have focused my efforts on new technologies that may create a new space for freedom.
He then goes on to talk about the internet, space colonization, and seasteading. I'm not really seeing the neoreactionary angle here. Am I missing something?
Ancient and not-so-ancient democracies have predicated the right to vote on such things as military service, land ownership, not being on welfare and other things. The idea is that voters should have a substantial stake in the republic (not saying that either predicate is a good, much less perfect, proxy for such a stake), not merely inhabiting it. Returning to that, rejecting "democratism" is the reactionary part.
Also freedom-first thinkers like Thiel (and me for that matter) can just say: sure I believe in democracy -- and the most effective way to get it is almost alway to let people rule themselves.
You can argue that that is playing with definitions -- but every republic since Athens that was worth a damn found ways to give individuals their space to do stuff that other people didn't like.
For the hardcore neo-reactionaries, democracy is not merely doomed, it is doom itself. Fleeing it approaches an ultimate imperative.
http://www.thedarkenlightenment.com/the-dark-enlightenment-b...
In the best case it leads to a realignment of the electorate.
In the worst case a lot of things go to hell, but he's a billionaire so he can always just up and move.
A pragmatic one.