Don't take it too much seriously. this is some sort of advanced autism that i've thought during the spare time. Also my english is shit, so please no bully.
First of all, what is the "Anarcho-Equestrianism"?
Is a mutualistic society based on an interpersonal ethic called "The Harmony".
It's not an ideology thought for the ponies, but for the humans.
It also holds some Stirnerian philosophy (what?! yep, keep reading)
What is mutualism?
https://en.wikipedia.org/wiki/Mutualism_(economic_theory)
Basically soft free market where the workers owns the mean of production. This concept strongly separate the Mutualism/AE from an anarcho-capitalistic society.
What is "The Harmony"?
Central in the AE society is the need for people of an ethic that helps to keep the world together, and teach the people how to avoid exploitations of someone else work.
The Harmony teaches humans how to respect other people and nature, so it can be divided in 2 branches:
-Interpersonal Harmony or "The Friendship": basically through the respect of the 6 elements of harmony: generosity, laughter, loyalty, kindness, Honesty and "magic" (which represent the ability of people to see the good in other people), workers are able to produce without exploiting each other, and people are able to live in a fully mutual respect.
The Harmony reject every form of violence and respect free speech.
-Naturalistic Harmony: As ponies are actively responsible of Nature, humans should do the same, by respecting the only planet they have, through the application of the 6 elements of harmony also to animals and plants. This doesn't imply that you are forced to turn into a vegan, but people should be more involved in the respect of the environment. Annual festivity dedicated to the harvest are welcome.
Why Anarcho?
Because once The Harmony has been established, and all the democratic activities are decentralized to small towns and group of people, there is no more need for the state. The currency holds value in itself, because the bits are made of gold.
So if this is an anarchist society, why the princesses are on the flag?
Because as I've already said this is an "ideology" made for humans, not ponies, and the princesses are symbolic: Celestia and Luna represent "The Harmony" as a concept and the cyclic nature of the world.
Why Stirnerian?
This is not an Ego-Anarchism ideology, but to reach "The Harmony" the society should have to despook itself from some concepts: the nationalisms, the race, the gender, the religions and the superstions, the dogmas, the ideologies and the identity politics.
It's not Stirnerian in the application of the "Harmony" ethics by the way, but AE accept the concept of ego and "the mutual willingness for the egos to cooperate", but reject ultimate selfishness.
People should ignore the concept of gender and race (as ponies treat equally the tree tribes and the other species), and act as fully equalitarian with no need for identity politics of some sort.
The equalitarian nature of AE doesn't imply that there are no recognized differences between people: you should do what you are good at! AE recognize the importance of meritocracy, the better you do the more you must shine. But AE do it in a context of equal opportunities.
How to reach this society?
I actually think this is a possible output for the modern society if the workers class gets more democratic power.
The only thing the people should do is to accept "The harmony" through culture.
not provided yet