Thiel actively supported one of the least libertarian candidates in US history. Whatever reputation he has for having libertarian views is nonsense.
No libertarian would try to control others based on his/her religious beliefs, and no libertarian would be remotely comfortable with any of the heavy handed stuff in Trump's platform.
In my view, what happened to Thiel and Musk is that they succeed in business and everyone starts respecting them and treating them like deities. They want to believe it is justified rather than simply people trying to manipulate them, which leads to a reinvention of self where they perceive themself to be a bit superhuman or important to the world. They act, they explore new areas, they act more. They usually do not experience as much reward from additional success in business, they are typically poorly socialized and fail to create a solid support network of people who know them and care about them. They realize money doesn't really help, fine food doesn't help, expensive possessions doesn't help. Even positions where they occupy a top hierarchical role end up feeling lacking.
What's left is the allure of tradition, religion, blood, war, progeny, and the trajectory of civilizations. They admire the brutality and decisiveness of medieval kings and the idea of theirs being destiny rather than luck. They then try to figure out how to believe they are deserving and suitable for the unique kind of destiny they realize can be theirs.
Most of us do not have to worry about hearing the voices they hear calling them to this destiny. One can see it on Elon's face. He's quick to sweat, quick to contemplate how his every decision will be more significant to the world than the entire lives of thousands.
Day after day of waiters, concierges, personal assistants, aides, advisors, trainers, masseuses, chefs, SVPs, etc. all at their absolute service. They must ask themselves again and again endlessly "what do I want? What do I really want?" Ultimately they realize that all they really want is to shape the world like so many kings or prime ministers or philosophers have. But theirs is a different skill-set. In spite of their desire they are not philosophers, not kings, not literati, not demagogues.
So they struggle to become that which they are not so they can do more than order a delicious lunch and pay for everyone else's and listen to everyone's flattery.
They want to shape the world with who they are, but part of them realizes it was luck and the are not as unique as they hoped. So they find ways to feel special like cultural supremacy, authoritarianism, buying favor with politicians or religious leaders, etc.