So the first thing to consider is that anarchy is a very diverse field of thought, so there isn't one answer to questions about it.
An anarchist society faced with violence from outsiders could:
- Form militias on a voluntary basis. Transitive hierarchical structure can be voluntary and compatible with anarchism (think of a volunteer fire department). Remember, the key is such efforts are not coercive in an anarchist community, they are voluntary and collaborative so they require the community having the will to organize for its own defense.
- Employ decentralized resistance / guerilla warfare. This can be extremely effective.
- If allies and neighbors are watching, engage in nonviolent resistance. This is difficult and requires getting the message out to other groups and the attacker's constituency to pressure them.
- Diplomacy. Anarchists generally don't support representationalism and prefer consensus, but communities can choose to empower diplomats and make deals with others when the time calls for it. This could be with other anarchist communities, other states to ask for aid, or even with the attacker. Building solidarity with like minded and compassionate communities can endanger the attacking group's reputation and resources, and can be a powerful deterrent to an aggressor.
Remember that an attacker wants something. If they aren't getting what they want out of a conflict, or if the costs are greater than what is gained, they are likely to stop pursuing it. Anarchist communities likely have different values, and resource extraction is the most likely reason to attack such a community; making it extremely difficult or impossible to do that is something an organized community can achieve.
Think about Vietnam; while Vietnam was and is not anarchist or non-hierarchical, a decentralized military strategy with deep support from the population led to victory over a technologically superior invader. For an example closer to anarchy, you can read up on the Zapatistas, who employed decentralized resistance to the Mexican government and won.
Last, I want to add that the above is more or less true of any community or country that is attacked by a larger force, whether they are communist, or capitalist, or stateless. Economic and social structure are not going to protect any group from being attacked, and doesn't guarantee victory no matter how organized the defense may be.
Transitive wasn't the best term to use, you're right to ask about that - I was referring to structures that are temporary, voluntary, and established as necessary. Non-hierarchical communities can form such voluntary hierarchies for specific tasks, much like the fire department analogy.
Your comments seem to question the resilience of smaller, less militarized societies against well-resourced, aggressive forces. Unfortunately, the vulnerability to more powerful entities is not unique to communities practicing non-hierarchical or alternative systems; it's a universal issue.
Examples like the Zapatistas, India's independence, and Vietnam's resistance against a superpower demonstrate that less militarized societies can sometimes successfully resist more powerful adversaries. These examples don't guarantee success but show that various forms of resistance can be effective.
An ideal anarchistic community focuses on mutual aid and sustainable, non-coercive living. They, like any small community, are susceptible to violent disruption or displacement by larger hierarchical entities. The fear of warlords or similar figures, as you mentioned, essentially acknowledges the ever-present human tendency to consolidate power.
The Doukhobors offer another insightful case study. They're not anarchists due to their patriarchal Christian family structures, but their community-oriented, pacifist lifestyle echoes anarchist ideals. Historically, they've been displaced by the state due to their rejection of many governmental norms. Wherever they resettled, they reliably transformed inhospitable land into productive farmland. Some argue this cycle of displacement and land cultivation was strategically orchestrated by the Canadian governmen to exploit their agricultural expertise. In their case, they demonstrate resilience instead of resistance.
It's common for people encountering anarchist philosophy for the first time to question its practicality against militaristic threats and it's a valid question. But the harsh reality is, regardless of a society's structure or philosophy, it remains vulnerable to aggressive entities with superior military resources.