I'm referring to his association with a certain milieu of people who are important figures in the development and promotion of what is today termed the alt-right.
Association with movements like that (or the others I mentioned) is sort of special. Movements like the alt-right are different from (for example) mainstream Christian conservatism or Randian Objectivism or democratic socialism.
Totalitarian movements whose goals would be considered insane or evil by a large number of people adopt the structure of a manipulative cult. When you encounter the Scientology guy on campus he offers to give you a weird kind of personality test. You have to be pretty deep in before you find out about galactic emperor Xenu.
The outermost surface of the alt-right (termed the alt-light in its own terminology) are people who superficially advocate nationalism, question political correctness, and so on. A layer below that you have a more hard-core layer that introduces racism, explicit anti-democratic strong-man politics, and misogyny. A layer below that you have the hard core of the movement where you find explicit advocacy of absolute totalitarianism, terrorism, and genocide.
Maybe I'm wrong but what I see is an onion that looks like:
Peter Thiel -> Donald Trump, Steve Bannon, Milo Yiannopolis -> Richard Spencer -> Andrew Auernheimer, 4chan /pol
The people on the right hand side represent the true beliefs and goals of the entire onion. You see it revealed in things like the Unite the Right rally in Charlottesville where the layers mix.
Compare this to for example Randian objectivism or democratic socialism. Everyone in those movements more or less espouses the same ideas. There's no onion because there's not much to hide.
In general when I see a movement with this kind of structure where the innermost people seem to espouse different ideas than the outermost I see it as a huge red flag. What are they hiding? The other thing about movements like these is that if you associate seriously and persistently with the outer layers of the onion I assume you probably know about and accept the inner layers too.
I was deeply saddened and frustrated when I saw evidence of Thiel's backing of that movement. Zero to One is still by far the best book about business I've ever read, and I found myself agreeing with I'd say about 90% of it. Thiel is also one of the few people who has seen what I've seen for years, namely that core technological development (what I call fundamental innovation) has slowed since the early 1970s. I rationalize it by acknowledging the human capacity for compartmentalization. It's possible for someone to have very rational views in one area and be completely nuts in others.