The other people either accept the legitimacy of the main laws of the system, do not see a viable alternative, or just do not dare to rebel openly. The common willing or reluctant acceptance of the authority of other people to make the rules and give orders is the core of the power of the capitalist social order.
The people who label themselves anarchists are the first of all rebels. All of them reject the capitalist social order. Through expression of their opinions and their various activities, they challenge the legitimacy of this system one way or another and incite other people to rebel.
There are many kinds of anarchists and other anti-authoritarian anti-capitalists, and their subversive activities are of a wide spectrum. While some are more effective than others, only very few actually damage the de-legitimacy of the capitalist system... or frighten people into supporting it (like the primitivists and the bombers/arsonists).
Some challenge the viability of the system's existence due to ecological problems and through that discredit the capitalist system in the eyes of those who worry about that sort of thing.
Some challenge the system by criticizing it for infringing the basic human urges for Freedom & equality & solidarity that even the capitalist system pretends to support, in its twisted way.
Others even do things like making their opinions known to the public and by various actions, more or less direct, more symbolic or concrete.
Some do it even in an organized way...
Nearly all anarchists know that the opinions of the people who have an interest in putting an end to the capitalist system do count.
Nearly all anarchists do try to influence the opinions of other people in one way or another. However, even among the more serious anarchists, only very few understand the dynamics of the system of opinions of human beings... Even among these the basic factor that is common to all the specific valuable tactics and strategies that do contribute to our common cause - the influence on the system of opinions - is not clear.
The most important facts about the system of people's opinions is that we have a plethora of opinions, we can have opinions that are not compatible with other opinions we have or even in contradiction to them. Within the opinion system, opinions can be more central and dominant than others... but their relative position can change according to changes in circumstances and emotional climate.
Just for example:
A classical study in the 1960s examined in the US the relationship between stated opinions of the owners of small food-serving businesses about their agreement to serve oriental clients, and their actual behavior. After collecting the opinions, clients with an oriental appearance came to these businesses. They found that most of those who stated to the opinion-collectors that they would refuse service, acted in a contrary way to the stated opinion.
The more we are aware of the fluidity of the system of opinions, the more we can effectively influence people in specific situations, and contribute to more fundamental changes in other people.
When we are aware of the dynamics of the system of opinions, we can contribute more effectively to the future functioning of people's opinions in specific situations and in a time of social crisis, uprising, and the revolution.
Thus, our main task is not to convince the majority of the exploited people that our anti-authoritarian, anti-capitalist revolutionary opinions are correct, but to influence their system of opinions to include these opinions as an option (in other words: not to change the dominant opinions of accepting the present social order, but to sow the seeds of the opinions we hold in a recessive position).
Our contribution to the development of doubts present in people about the present society or the main aspects of it will result, in a time of crisis and revolution, in an exchange of places between the dominant pro-capitalist and the recessive anti-capitalist opinions.
Developing/promoting doubts in the authoritarian pro-capitalist opinion and Developing/promoting anti-authoritarian anti-capitalist alternatives.