Personally, I do not agree we need any kind of minarchist state. But that was not the original question you raised.
This is a popular Venn Diagram, and a good starting point I feel, for the breakdown of different political concepts as discussed above:
Libertarians might encapsulate Classical Liberalism, Minarchist, Paleo-Conservatism or Voluntarism, but cannot really be applied to Modern Conservatism, Liberalism or Total Socialism. Though it can be said that the NAP is heart of the Libertarian philosophy, Libertarians would have to admit that even the least invasive of these classifications into someones life is still an invasion, and only true Voluntarism does not ethically violate the N.A.P., it would generally go to underline the saying “I was a minarchist till I ran out of excuses”.
Look into these classifications as a base line. Then your question exists in several different shades of Libertarian thought, and even beyond.