There will ALWAYS be violence. That is a given. The difference is between aggressive and defensive violence. Defensive violence is always morally permissible, and one could argue that it is a moral imperative.
The difference is that in (most of) the other religio-political ideologies you list, the INITIATION of violence is the basis of society and the basic rule. That's a very big difference from using violence for defense (i.e. Anarchism).
Anarchism doesn't preclude people from associating under some set of ideologies, e.g. anarcho-syndicalism, anarcho-communism, etc. The only thing it precludes is the initiation of force/violence.
So, if you want to live under Communism, you can. Just as long as you don't force others to do the same. Ooops! Guess not, because that's what Communism is - violence.
So perhaps Democracy? Ooops! Nope. That's the tyranny of the masses.

A mob gets together and forces other people to do what it wants.
Then maybe Republicanism? Ooops... United States of America, Democratic People's Republic of Korea, Union of Soviet Socialist Republics, etc. etc. They don't seem to turn out very well either.
Etc. etc. etc.
But Anarchism doesn't prevent anyone from banging their heads against the wall. All the others FORCE you to bang your head against the wall.
Anarchism is almost always maligned and misrepresented. Grouping it with the likes of Democracy and Marxism is misleading. It has no resemblance to any of them.
"Capitalism", on the other hand, describes normal economic activity between people. It has many bastard, deformed children, with each one uglier than the last. Perhaps it's most popular bastard is "Corporatism". It bears a striking resemblance to its older sibling, "Fascism". Another ugly bastard is "Crony-capitalism", which really makes a mockery of it's descriptive parent. But really, they're all so ugly that they're almost impossible to tell apart.
HOWEVER -- All Capitalism's bastard children REQUIRE a religio-ideological framework to function. They cannot survive under Anarchy.