> Normally libertarianism has an 'exception' for defense because it's a pure commons. There's no obvious way to have private sector military due to the nature of wars and invasions. Indeed, the government having a monopoly on violence is a core part of libertarian thinking.

This is an entirely parallel subject. The monopoly on violence (which is just a concept in the theory of state, not a uniquely libertarian concept) doesn't imply a hawkish foreign policy outlook. Put another way: the libertarian perspective (even the minarchist variants) don't entail the kind of aggression that Thiel publicly advocates.

Being a hawk on China (e.g., extolling the US MIC to take a more aggressive stance in territorial disputes and information warfare) is a very conservative, not libertarian, position.