The important thing to remember about Gnomes is that, at the core of their society, they are refugees. They are not native to the mortal world, even if they have lived there for generations. They originally come from, and still have a strong connection with, the realm of the Fey.
The important thing about the realm of the Fey is that, no matter how whimsical and riotous it may seem, it most definitely has rulers: the Lords of the Fey. Demi-godlike beings, they are whimsical and riotous, quite often towards their own subjects.
This means that no matter what society Gnomes find themselves in, there is still a slight sense of unreality, of play-acting, among the Gnomes. No matter how awful or mad a tyrant in the mortal realm may be, they don’t compare to the rulers their ancestors had to deal with. They don’t see the institutions and governments of the mortal realm to be sacred, not in the ways that Humans and Dwarves do. This lets the idea of Anarchy be much more appealing to Gnomes than it might to others. They also share the passion of creation with Dwarves, meaning that when Gnomes do commit to Anarchy, they commit with a whole heart.
The only thing preventing Gnomes from being the backbone of Anarchism is their constant need for new experiences. They may fall in love with Anarchy more easily than most, but as a matter of survival they may fall in love with something else just as easily.
Gnomish Anarchists tend towards the Individualist, Mutualist, Environmentalist, Egalitarian, Free Marketeer, Illegalist, and Poetic traits.