I was thinking about the theory of libertarianism, not the political party that calls itself Libertarian. The logical conclusion is that libertarianism must lead to anarchism, I see no way around it.
That's not true. At a minimum, libertarianism requires a robust court system that must be funded with taxes. Why? Because most disputes would be handled between individuals rather than the government acting on behalf of the people.
For example, in an extremely libertarian world, there would be no pollution regulations. However, one of the key aspects of libertarianism is that you are free to do whatever you want so long as you don't harm others. So, there would be lawsuits galore about the affects of pollution and people/companies would be forced to pay.
You would also need an army, police, jails, etc. that would need to be funded by taxes.
You wouldn't necessarily need the departments of: agriculture, education, commerce, energy, HHS, HUD, Interior, Labor, Transportation, Treasury, or Veterans affairs.
You would need the departments of Defense, Homeland Security and Justice. So, still a government and not anarchy.