"...apart from direct antifascist action?"
what is the problem with "direct antifascist action"? isn't that - direct action - one of the core tenets of any anarchistic perspective?
though ultimately what i would find more interesting is a discussion of "seizing the state" (by anyone) and the relevance of that to anarchists.
"As anarchists, we don't want to form parties, as they are hierarchical organizations. This would let the fascists take the state with their party/parties in such a way that they'd ban the anarchist organizations"
From above, i sense a misunderstanding such as anarchist refusal of forming hierarchical organizations means letting other parties to increase their power by capturing state apparatus or any other way. This is not the case of course. Problem here is to find ways of building a force that can counter such initiatives of fascists or any other groups, like isolating them so they can't appeal to people, or distrupting state's organization in a way that even if it keeps existing formally, it has practically no control over an area.
Any anti-fascist group faces the problem of countering fascists whether they organize through hierarchical lines or not. Fascist conquest of state and subsuquent repression doesn't come from the fact that anarchists refuse creating hierarchical organizations, it is because they fail to create a force powerful enough to stop fascist initiatives. If it were otherwise, i mean if it is actually because they refuse to organize hierarchically, then being anarchist would not make any sense since it would mean impotence.