Dwarves are not the most obvious candidates when it comes to who would be an Anarchist. They value law and order, tradition, and imposing their will will upon the environment, as seen in their cities and their crafts. They also hold grudges, as seen in their attitude towards Elves, Goblins, Orcs, a lot of Humans, and anyone else who annoyed them, even generations ago.
But this impression does not reflect the stubborn, even cantankerous nature of the Dwarves. There is a reason that family ties are so important in Dwarf society, and that the society seems to be centered around small autonomous city-states. For every stubborn Dwarven king and Master of the Mine, there are hundreds of equally stubborn Dwarven subjects and miners, equally capable of asserting their own will, and holding grudges against those who use them ill.
If Dwarves have a true defining characteristic, it is a single-minded pursuit of their vocation, whatever that is. They will continually may keep practices and traditions that have served them for hundreds of years, not being swayed by the fads and fashions of other races. But while Dwarves may be sentimental towards family and lost homelands, this sentimentality does not extend towards how they live their lives and do their work. Dwarves with keep what works, but they will also always be on the the lookout for something or some method that works better. If they find something better, like and new way of organizing society, they will embrace the new as readily as they embraced the old. And the heavens help anyone, be it King, Priest, or Master of the Mine, who gets in their way.
Dwarven Anarchists tend towards the Mutualist, Free Marketeer, Philosophical, and Syndicalist traits.