Anarchism is not non-political. Nor does it advocate a retreat into prayer, self-indulgence or meditation, whether or not one contemplates one's navel or chants mantras. It is simply hostile to parliamentary or party politics. The only democracy it thinks valid, is participatory democracy, and considers putting an X on a piece of paper every four or five years is a sham. It serves only to give ideological justification to power holders in a society that is fundamentally hierarchical and undemocratic.
Anarchists are of many kinds.
They have therefore suggested various ways of challenging and transforming the present system of violence and inequality-through communes, passive resistance, syndicalism, municipal democracy, insurrection, direct action and education. One of the reasons why some anarchists have put a lot of emphasis on publishing propaganda and education, is that they have always eschewed party organization as well as violence. Anarchists have always been critical of the notion of a vanguard party, seeing it as inevitably leading to some form of despotism. And with regard to both the French and Russian revolutions history has proved their premonitions correct. A consistent critique of anarchism offered by Marxists is that it is Utopian and romantic, a peasant or petty-bourgeois ideology, or an expression of millennial dreams.