Thiel has been a big backer of the Seasteading Institute, which seeks to build sovereign nations on oil rig-like platforms to occupy waters beyond the reach of law-of-the-sea treaties. The idea is for these countries to start from scratch--free from the laws, regulations, and moral codes of any existing place. Details says the experiment would be "a kind of floating petri dish for implementing policies that libertarians, stymied by indifference at the voting booths, have been unable to advance: no welfare, looser building codes, no minimum wage, and few restrictions on weapons."
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To be honest, I think many (most?) independent voters in the US (who tend to disagree with the democratic & republican parties on many issues) are probably closer in political thinking to Libertarians, and would probably be better served by supporting the Libertarian Party than by continuing to vote for whichever republican/democrat they think is the lesser of two evils in any given election. Doing that just guarantees that they'll end up with another democrat/republican in office, which isn't what they really want anyway...