The field of Austrian economics has gained some popularity in non-economist circles. This is partially because many people feel that government has intruded too much in their lives, and partially because Austrian economics seems more accessible to the lay person - no complicated mathematical formulas and whatnot. Such people find they agree with many of the policy conclusions of practitioners of Austrian economics. The policy conclusions are usually: intervention by the state in the market created XYZ problem, so the fix is to get the state out of the market.
News flash: Neoclassical economists often have the same conclusions. Price controls, for example, are always bad because they create gluts (price floors) or shortages (price ceilings). Neoclassical economics shows that markets were very well, most of the time, and most problems come from interference with the market.
So the policy conclusions of the Austrian economists are not unique. Economists of the Austrian persuasion don't start by saying "the state is the cause of the problems!" That's actually a conclusion of a rigorous analysis of economic principles and history. Economists of different schools of thought may come to different conclusions because the paradigms are different. This is especially the case in macro and monetary economics.
Yes, many Austrian economists are aligned with libertarianism. Still more might say they are "classical liberals" of the Smithian/Lockeian sort. And there is probably a self-selection bias there. I know what Hayek's and Mises' positions were vis-a-vis state intervention, and this certainly attracted me to the study of Austrian economics. (Although I think Hayek is too much of a statist). But the problems of state intervention are a conclusion of Austrian analysis, not an axiom.
So, Austrian economists is not unique because of its policy conclusions. What separates it from the crowd is the method of analysis, and the focus on individual decision making with its attendant knowledge problems. The method is praxeology, which is essentially logical reasoning from a few basic axioms - the primary one is "humans act." Knowledge problems are probably what made Hayek famous (Use of Knowledge in Society, AER, 1945). Finally, Austrians view competition as a process, not a state of being. That makes the Austrian view of Industrial Organization a little different than the standard Neoclassical take on it.
Do libertarians follow Austrian economics? Yes, it appears they do. And the less educated they are about it, the worse it is for Austrian economists. The last thing we want is nut-job gold bugs aligning themselves with a school of thought because some within that school suggest a return to the gold standard would be stabilizing. In fact, within the Austrian school, this is a most controversial position to take.
I don't want Austrian economics to be inaccessible. I think everyone should read Economics in One Lesson (Hazlitt) or Economics for Real People (Callahan) both available for free (as a .pdf) from Mises.org. Ludwig von Mises himself thought economics should be studied and be accessible to everyone, not just professional economists. What I want, though, is for people to spend the time and really learn the material before agreeing or disagreeing with policy conclusions.