Libertarianism is the logical outcome of a single core belief, the Non Aggression Principle or NAP. In its simplest form the NAP says that people should be allowed to live their life as they see fit as long as it does not involve the initiation of force against the life of another or their legitimately owned property.
The ONLY things that Libertarianism is fundamentally against are the initiation of violence and coercion under threat of violence.
The left claim that Libertarians are against taxes, welfare, state services, etc, etc, but that is not actually true, what Libertarians are against is the use of force to impose these things on people.
As Nozick pointed out in, the much neglected, final part of Anarchy, State & Utopia, a Libertarian society is the most tolerant and accommodating of any conceivable society.
If a group of people wish to establish their socialist utopia (or a fascist one) they are welcome to. They may legitimately assert that a certain area of land that they collectively acquire is socialist (or fascist) and that the rules of socialism (fascism) apply in that territory. Anyone who wants to live under these rules is free to do so. The only things that a Libertarian society would prohibit are, forcing people to live in this area (under those rules), or preventing people from leaving the area (and the rules) if they decided that they no longer want to live that way.
Likewise if a group of people wish to establish a Christian (Or Jewish or Islamic) fundamentalist state, they are welcome to. People who want to live by that code are free to do so. The only thing that Libertarianism insists on is that they force nobody to do so against their will and that they do not force anybody to stay who wishes to leave.
The essence of Libertarianism is voluntarism.
Libertarians are not against Socialism, or any other political or religious belief system, they are simply against forcing people, under threat of violence, to live in a way that they don’t want to.
The same cannot be said for Socialism, which is a set of beliefs that require people to live in a certain way. Socialism is not the voluntary choice to adopt progressive taxation, univeral welfare provision, egalitarianism, etc. It is the imposition of these beliefs under threat of State violence.
Socialism does not allow people to own areas of land and chose different rules by which they will live their lives. In a socialist society nobody can choose to keep all their earnings and pay for the services they want, to take out insurance (or not) against misfortune and to give to charity what their conscience tells them is a fair amount.
If socialists believed that people would live by their beliefs without being forced, then they would have no problem with Libertarians or a Libertarian society, it would welcome them.
The problem they face is that, when given the choice, very few free people actually choose socialism. Nozick examined this in the essay “Who Would Choose Socialism” published in his book Socratic Puzzles.
He asks “Approximately how many people would choose, under highly conducive conditions, to live under socialism?” He bases the figure on the percentage of people in Israel who have chosen to live in a kibbutz and explains why this is the optimal scenario for voluntary socialism. He concludes that the figure is “about six percent”.
The Libertarians are very happy if 6% (or more) of people want to live this way, as long as they don’t force anybody.
The socialists on the other hand want the 94% of us who wouldn’t choose to live that way, to be forced to ! (it’s for our own good you know, we are just too stupid to see it!)
The same arguments can be applied to Fascism, Islamic Fundamentalism and any other political or religious doctrine that demands that everyone live in a certain way.
If you object to Libertarianism, the ONLY thing you are objecting to is the freedom for people to choose for themselves how to live their lives AND you are accepting that whatever alternative political view you propose, it would fail without the use of force.