If there's any side with a significant risk of being non-scientific, it's the anarchists. You can blame statist political scientists, sociologists, and economists with being amoral technocrats, but there's definitely a system in place for them to update their opinions about social organization based on facts. Consider an article like this
. The authors are criminologists with grants from the U.S. Department of Justice; basically, they're academic cops. So it's pretty clear that they are statists, and that any results they reach or any other research they support is influenced by that belief. Nevertheless, they follow a research methodology common to all science: they propose a model (about the way that proposed weapons bans influence manufacture, prices, and ultimately murders committed with a certain weapon); then they discuss the extent to which data supports this hypothesis (the data agrees, but it is also consistent with random fluctuations, e.g. from causes uncontrolled in the data); finally, they address explanations that were not covered in their research in a section for suggested future research. Nothing about that way of doing things favors one set of ideas over another. The authors have very little room to introduce their own biases into the research. From among many ways to design their study, they might choose the one that favors their position, but the overall process of the research (among statist social scientists) includes discussions about the validity of statistical methods and experimental designs for making a given decision. Other than that, they can't change the data and they can't (on their own) change the set of research methods that are considered valid. So this approach prevents researches from arguing for a position just because they prefer it, just as the scientific method should.
This is the common methodology among academic social scientists, most of whom are not anarchists. The leading anarchist or free market thinkers of the past, by comparison, do not ground their arguments in such inscrutable methods. Marx, for example, and most socialist anarchists who followed him, base their opinions on interpretation of major historical changes, a methodology that is very easy to abuse. Market anarchists are no better: the axiomatic approach of von Mises is basically a commitment to being non-scientific. Having said that, there are anarchists, of any variety, who do use statistical methods in their approach to discussing social organization. Still, there's a tendency among anarchist social scientists to avoid using the accepted experimental designs of their disciplines. Anarchy isn't non-scientific, in its own right, but anarchists haven't made the same commitment to scientific methodology as mainstream economists, social and political scientists.