At the heart of libertarianism is the claim that in order to fully enjoy your natural rights you must be free of coercion. That is, you are not subject to the claims of other people either directly or indirectly. The only direct claim a person has on another person is the enforcement of a contract. Similarly, you can demand that whole society respects your autonomy and property rights. Otherwise, no person in a libertarian society has a claim on any other person in the society.
Simplifying it, the libertarian society assumes you have absolute dominion over yourself, outside of the narrow exceptions for the enforcement of contracts and the defense of private property. More important, maybe most important, members of a libertarian society have an obligation to respect the autonomy of others. The social contract, if you will, gives members the maximum liberty, in exchange for the maximum amount of minding your own business.
Hans Hermann-Hoppe identified two unsolved problems within libertarian theory that he has spent a long time trying to solve. One is that there is no way within libertarian theory to go from our current societies to a libertarian one. The other problem is there is no way within libertarian theory to police a libertarian society. The non-aggression principle rules out coercion as a way to keep people from straying from libertarianism into something like socialism or even communism.
It is the first problem that has occupied the minds of libertarians. How can we get from where we are now to even a few steps down the road toward paradise? One effort has been to convince people to become libertarians. Proselytizing has always been a central part of the movement, which is why many people outside of the libertarian subculture view it as something like a cult. The libertarian, like the vegetarian, is always ready to announce his membership in the cause.
The proselytizing has always come with an eye on politics. In theory, libertarians must reject the premise of liberal democracy. The closest they can come is some sort of democratic process for settling direct and indirect claims. Otherwise, there is no role for the state so there is no reason to have elections. Even so, libertarians have tried to use the democratic process to change the law in their favor. The legalization of drugs, for example, has been a main cause of libertarians.
A lot has been made about the effect this has had on conservatism. Way back in the last century, Frank Meyer cooked up a new formula for the American right that brought libertarians into an alliance with traditionalists and neoconservatives. This Cold War coalition would make up what was called the conservative movement. After the end of communism, this coalition fell apart. Today it is nearly impossible to see the difference between libertarianism and mainstream conservatism.
Something else happened during the last century. The contact with mainstream liberal democratic politics deranged libertarianism. Some libertarians, the left-libertarians, transformed into corporate libertines. In exchange for a comfortable lifestyle, they promote every degenerate fad of the left in the name of freedom. The left-libertarians have been enthusiastic for every subversive cultural fad, as long as it came with fat donations from corporate sponsors.
Right-libertarians have largely avoided the cultural issues, instead focusing all of their energy on the power of the state. Ron Paul has been the best known of the bunch, fashioning a political career as a platform to promote libertarianism. At the heart of his argument is the assumption that once the state is removed from the lives of people, the cultural questions will answer themselves. It is the state that puts its thumb on the cultural scale, creating the culture war.
It is a nifty bit of logic, which turns the old Marxist formulation on its head. Marx said that once you get the morality right, there is no need for politics. That is, once everyone has the same morality, there is no need to debate public policy. The friend enemy distinction goes away as we all share the same goals. Ron Paul argues that once you get the politics right, the moral issues settle themselves. Without an active state, there is no need for culture and therefore no culture war.
The last ten years has provided a test for that theory. It has also brought us back around to that second conflict within libertarianism identified by Hoppe. Over the last decade, corporations have assumed greater power over the lives of citizens and they have become active in directing the culture of society. On the one hand we have non-government elements of society that are trying to coerce others. On the other hand, that coercion is specifically over cultural issues.