Conflict between the socialist oriented and market oriented camps within anarchism can get very tedious. Many anarcho-communists and anarcho-syndicalists appear to emphatically claim that market anarchism isn't truly anarchism, that opposition to private property and capitalism is a requirement for one to be an anarchist, conflate currently existing political and economic systems with a free market and sometimes even defend welfare states as if take the edges off of the alleged evils of capitalism. Some anarcho-capitalists appear to get baited into functioning as vulgar libertarians or they generally associate themselves too closely with contemporary conservatism and therefore end up defending currently existing corporatism as if it is the result of a free market, claim that all forms of socialism are statist political systems, defend paleoconservative positions on issues such as immigration and romantisize feudalism and colonial America.
The bulk of the debate between the two sides consists of a language barrier, semantics and quibbling over property. There is a language barrier over terms such as capitalism, socialism, communism, anarchism and libertarianism to the point where any true meaning is rendered obsolete. Each side suspects that the other side are merely authoritarians in disguise, and sometimes the suspicion is entirely justified (with some social anarchists functioning as state-socialists and some anarcho-capitalists functioning as conservatives). The more that each camp acts foolishly intolerant and monopolostic, the more likely they are to be pushed back into the statist paradime due to reactionary sentiments, leading to the use of political means to dominate against their alleged enemies. Sometimes they spend more time critisizing eachother than they do critisizing contemporary statist ideologies.
Capitalism has different connotations to the various camps. Some consider capitalism to be the current system, some consider it to be separation between labor and ownership, some consider it to be private ownership of the means of production or the extensive use of capital and some consider it to be a spontaneous order resulting from the voluntary and mutually beneficial interpersonal relations between people in the absence of a central planner or state through a process of free trade relations and competition. Socialism has different connotations as well. Some consider socialism to be worker ownership of the means of production, some consider it to be state ownership of the means of production and some consider it to be some sort of egalitarian free market. There are nearly endless semantics over the meanings of the terms which avoids a real discussion and debate about the actual principles that people advocate. These semantic conflicts even exist within each respective camp, as some market anarchists have abandoned the term capitalism.
Etymologically, anarchism simply means "no rulers". Anything that is without rulers is therefore anarchic by definition. Any philosophy that is opposed to rulers is an anarchistic philosophy by definition. Whatever additional features they may have is only a matter of flavor. On a fundamental level, all anarchists of any type oppose the institution of the state. Anything else that they may support or oppose beside the state is comparatively inconsequential, although it is of course true that non-state institutions may sometimes qualify as examples of rulership. So it does make some degree of sense to say that anarchism is more than mere consistant/radical anti-statism, even if one wants to quibble that such institutions would qualify as states anyways. One way to put it is that anarchists are opposed to crime or plunder in general as a matter of principle, and more large-scale manifestations are merely the institutionalization of crime or plunder. In either case, there is no reason to ostracize people who truly do oppose rulers from the anarchist movement just because they have perhaps a somewhat different flavor than one's particular camp.
The issue of property is the main area of conflict. The property debate has been going on forever. Some social anarchists seem to think that private property is either a product of the state or inevitably leads to a state. Private property may be thought of as either a legal construct or a form of exploitation that precedes and leads to the formation of states. Of course, one cannot logically hold both positions at once, since that would be like taking both sides of a chicken/egg debate at once. Market anarchists tend to define private property in terms that should actually appeal to a socialist, which is that legitimate private property is the product of labor - a labor theory of property aquisition. How can a socialist oppose labor when that is supposed to be their forte? If consistant to their principles, the market anarchist does not support all legal private property titles, for they have an independant standard of justice in property aquisition that would delegitimize currently existing conditions. In short, they oppose the currently existing legal construct. The vulgar libertarian, however, does fall into the trap of defending all or some illegitimate portion of currently existing private property titles and buisiness arrangements.
On the other hand, complications arise over the value of labor, as social anarchists tend to cling to some kind of labor theory of value. This is problematic because it doesn't adequately take into account the labor of the enterprenuer, the dynamic nature of prices and the factor of time in general. Contemporary market anarchists usually have discarded the labor theory of value for a subjective theory of value and theories of time preferance. However, if one observes individualist anarchists such as Benjamin Tucker who still held to a labor theory of value, it would seem to be that case that the such people thought that a free economy would naturally reflect a labor theory of value. So in this sense classical individualist anarchists are entirely supportive of laissez-faire and only disagree with more contemporary market anarchism in terms of what they think the outcome of a free market would be. More contemporary individualist anarchists have merely modified the position in light of changes and improvements in economic theory. If one takes a 19th century individualist anarchist and merely substitutes the subjective theory of value in place of the labor theory of value, one essentially has a contemporary market anarchist.
Diehard social anarchists oppose what they consider to be private property. They often make a distinction between personal property and private property or between possessions and property. They tend to have a principle loosely based on "use" of property that is supposed to be more limited than the extent of control and amount available to the individual that private property allows for. It would seem that there is a threshold of requirements for property ownership with perpetual use at one end and perpetual ownership in the absence of use on the other. If they are pushed and in a logical state of mind, the social anarchist will not tend to condone a standard of perpetual use and the market anarchist will not tend to condone a standard that allows one to hold a title to blatantly abandoned or unowned property, for each of those standards leads to endless absurdities and may justify clearly wrong and exploitative scenarios.
Perpetual use is an absurd criteria for ownership, for it would imply that as soon as one parks their car somewhere then it is no longer theirs and therefore someone else may expropriate the car for themselves. In short, it would justify theft. On the other hand, there are problems with titles to ownership of property, particularly land, that has blatantly been abandoned or neglected by the person with the title to ownership and while there simultaneously are actually other people who actually actively labor upon it. Intergenerational or perpetual ownership over property that one makes no use of yet others do leads to fuedalism. Surely future generations of people should not be bound to a nullified claim of ownership by someone else, some rich aristocrat who no longer contributes in any real way to the upkeep of the property or makes any use of it at all. In order to resolve the issue, some process of identifying or clarifying whether or not the property in question is abandoned by its original owner would make sense. It should be noted, however, that this does not necessarily justify the claims of the geolibertarians, who erroneously conclude that private land ownership is illegitimate and/or there should be collective land ownership as a universal standard.
When the absurdities resulting from the idea of perpetual use are pointed out, the social anarchist will often proclaim "general use" to be the standard for ownership. But general use is very vague, leaving open a range of possibilities. It would seem to be the case that what constitutes general use would have to be agreed upon or arbitrated, quite possibly varying from organization to organization and/or community to community. If this is conceded, then the only real difference between the two sides is a matter of what type of voluntary precedent one personal prefers. So long as each side remains at least passively tolerant of the fact that perhaps different communities or organizations of people will have somewhat different standards, then there is no reason for conflict. Free association resolves the problem. If a standard objectively ends up being more sucessful and efficient through voluntary interactions, then it will tend to win out in the dynamic and evolutionary process of trial and error that is inherent in free association and competition.
Social anarchists demand worker ownership of the means of production. If consistant to the principles of voluntary interpersonal relations, the market anarchist has no choice but to support the liberty of individuals to voluntarily form worker's collectives and opt out of or secede from other particular organizations. If the social anarchist is likewise consistant, they have no choice but to support the liberty of individuals to voluntary form into employer-employee relationships and opt out of or secede from their worker's collectives. If one is forced into or out of such associations through force or the threat thereof, then they would effectively become slaves. So long as neither side actually forces anyone into their prefered organizational structures, each side can mutually persue their desires without infringement upon others. In a sense, the key question to ask is: can I opt out of your organization/community/society? If not, then it is no different than a state. If so, then there obviously is not going to be absolute uniformity in terms of what particular organizations and types of organizations people choose to participate in, as everyone is not identifical in their preferances, traits and abilities.
An interesting cunundrum to present a social anarchist with is, "I want to be a wage slave, I want to work for a boss, so what do you do if I truly do choose to enter into a contractual relationship with someone for wages in exchange for my labor? Why can't I rent out the products of my labor if I sincerely want to? What if I want to opt out of the worker's collective and look for an employer?". If an individual is truly autonamous, then noone may legitimately force them out of this personal association or force them to remain in a particular association, whether it is a single individual or "the majority" or "community". Likewise, an individual should have the liberty to opt out of an employer-employee relationship and voluntarily organize with others into worker's collectives or other types of organization. One must recognize the liberty of even a single individual to secede from an organization. So long as one does not have any genuine debt or contractual obligations withstanding, they should be able to exit the association and persue other ones. That's precisely how free competition works, as undesired and inefficient modes of organization become obsolete by people's choices not to associate with or participate in them.
Forms of organization that are considered to be socialistic are theoretically possible options in a free market. This is something that some people from both the anarcho-capitalist and social anarchist camps seem to not want to aknowledge, each for different reasons and from different perspectives. The consistant proponent of voluntary interpersonal relations has a certain kind of tolerance that allows for those who disagree with them to opt out of their prefered organizations and voluntarily form alternatives. It's essentially a live and let live perspective: don't force me into your community or organization and I shall do likewise. Call it whatever one wants, the law of equal liberty, the non-aggression principle, decision-making in proportion to the degree that one is effected, etc., it's all essentially the same thing. Within the confines of the general principle, anything additional is only optional or preferential.
Philosophies and ideas in general evolve over time, and this is just as true about anarchism as it is about anything else. The economics and philosophy behind anarchism have evolved, sometimes into territory that is very market oriented. There is a progression and tree of sorts that can be traced from the most original anarchists to currently existing factions, including market anarchism. Mutualism can be seen as progressing to individualist anarchism and eventually into contemporary market anarchism, so claims that market anarchism has no place within anarchist tradition is false and ignores the variance that has always existed within the general movement. To try to cling absolutely to every single aspect of an obsolete theory from centuries ago starts to make one rather conservative, and in this sense some social anarchists have become blind traditionalists who are unwilling to modify their ideas in the face of new information. On the other hand, contemporary market anarchists should have a lot of appriciation for early anarchist tradition and be willing to see what they may have in common with more socialist oriented anarchists. They should understand themselves in historical context and aknowledge that certain segments of their philosophy wouldn't exist without those who came before them, the Proudhons and Bakunins and Tuckers and Spooners.
There is no rational reason for there to be the degree of conflict that currently exists between the different camps of anarchists.