—Omnilibertarian Rule Theory—
Institutions capable of systematically frustrating the inherent interests of those subject to them, are held to the same justificatory standards regardless of whether they are public or private.

Imagine the State forcibly prevented you from criticizing them. What if instead of actually hurting you for criticizing them, they exile you from your country. Does that make it better?
The answer is a clean no.

Now the fundamental question is, why limit this to the State? Any institution can act similarly to a State, or a government more generally, with or without the use of direct force.

Relative to Yoggism, relative to whether actions can be justified relative to others interests, and relative to the Anti-Abuse Principle, that actions inherently frustrating against inherent interests, we can explain the intuitions behind the idea that censorship, discrimination, and unfair treatment more broadly is bad, beyond just enforcement by government.
 

—What does it mean to be Free?—
What does it mean to be free? This is usually demonstrated by asking, is a person starving in a desert free? They are merely free to wander and die.

What if a person is born into a large company town owned by a crazy landlord who forces you to follow arbitrary rules for his own benefit, and if you break the rules you lose your home and are exiled?
This is a clear example of a non-State entity acting as a local government over a group of people, and as such this institution has the ability to threaten their freedom.

Under Yoggism, this distinction between the State acting upon you, and private entities doing so, may as well not exist. Actions that frustrate against interests, enforcing interest misalignment, is illegitimate and cannot be justified by any measure. This is true regardless of who is doing it.
Ethical evaluation is actor-neutral in this sense.

—The Basic Idea—
True individual freedom can only be gained if people have proportionate control over how they are treated by institutions that have the capacity to threaten their own interests.
Enforcement of interest misalignment, where people who's interests are not aligned with yours enforce their interests at the expense and disrespect of yours, are illegitimate.

Thus, certain things like freedom from being censored for criticism, are to some extent rendered universal across domains and institutions, private or otherwise. To be banned from a social media platform for criticizing that platform, or criticizing the government, may be entirely illegitimate. To be singled out and treated unfairly, is illegitimate.

Discrimination in public spaces, like restaurants or stores, is illegitimate and unjustifiable.
Being arbitrarily prevented from self-expression, where your actions aren't inherently frustrating against anyone, may also be illegitimate, regardless of if such abuse is done under the guise of employment, tenant-ship, government, paid service, or other such management.
 

—Why the NAP need not apply—
Here the right-libertarian Rothbardist sites the Non-Aggression Principle as the way to distinguish between coercive institutions, I.E. the State, and voluntary institutions, I.E. private companies.
The right-libertarian's claim is that the leader and owner of a company town has the right to all property in the town, and you being born there does not change that. He has no right to hurt you or enslave you, but he does have the right to kick you out at his own discretion.

There are two big problems with this. The first problem is that actions taken against people living in an abusive company town cannot actually be justified, not relative to interests, and not relative to anything else. They are enforcement of interest misalignment and represent in a Stirnerian sense, spooks against their own self-interest. As explained in Justification Ethics, such abuse and inherent frustration against their interests are illegitimate.

The only argument here is an attempt to somehow prove the town owner has an exclusive right over the town, in an absolute sense. This cannot be shown in a way anyone else is rationally required to accept.
The second problem is that this position is fundamentally anti-freedom, and this can be proven if we assume the meaning of freedom has anything to do with a subject's set of possible actions whatsoever.
 

—Self-Sovereign Prescription of Agency—
Imagine you are in a cage, there are armed guards that will shoot you if you try to escape. Everyone would agree here that you are not free, even though you technically have the freedom to attempt an escape, but since the consequence of such an action will result in death, it's not a real choice.
Now imagine all else is equal, but the guards are actually non-sentient robots, their creator long dead. If you try to escape, you still die. Are you free?

Again the answer is a clear no. Yet the libertarian is forced to concede that you are actually fully free, because no person is aggressing against you. You are not being coerced into doing anything according to them.
This makes sense to them, as they view freedom in a way that is anti-individualist, in the sense that it has nothing to do with the actual individual's ability to fulfill their own self-interest.
Instead, to them, freedom is based on what everyone else is doing. Not what you can do.
 

—Yoggism's Implications—
Justification Ethics as previously mentioned, shows some actions cannot be justified relative to interests, because some actions are inherently interest frustrating. This implies the Anti-Abuse Principle, which as previously mentioned is the idea that actions inherently frustrating to inherent interests, are illegitimate, and that enforcement of interest misalignment is the root of illegitimacy.

Inherent interests as used here and elsewhere refer to interests that act as a conduit for other interests, where an interest's frustration causes frustration of other interests as an interdependence. This is the concept of interest entanglement.

Interest misalignment is the most relevant term here, and it can be demonstrated in the example of the landlord owner of a company town. His interests and your interests are entirely misaligned, and he is enforcing his interests upon you, in the sense that your interests are actively frustrated for the benefit of his.
This enforcement of misaligned interests against your own, in a Stirnerian sense, represents a spook against your own self-interest and autonomy.
 

—Conclusion of Omniliberty—
The conclusion here is simple. That which is bad, is bad regardless of the entity executing it. Censorship, unfair treatment, discrimination, and similar abuse, as well as things like murder and stealing, are illegitimate whether done by a State or a private entity.

Large tech companies trying to shut people down, or enforcing their own rules unfairly, is abuse. A libertarian could claim that abuse of authority and banning people from platforms who didn't violate rules, is actually a contract violation, but merely adding exceptions and extra rules stating they "have final discretion and can act against you for any reason" doesn't make it not abuse.

This is what the "omni" in omnilibertarianism means, liberty in all domains. Fairness in all rules.
 

—Rothbardianism is Collectivism—
Murray Rothbard is the founder and leading theoretician of anarcho-capitalism and right-libertarianism. Rothbardian libertarians claim to be individualist, but this is a farcity.

To be held under interest misalignment as described, to be 'functionally enslaved' to the Lord of a company town, is to be controlled by a larger entity, to be treated as nothing more than a pawn in a larger system beyond your own control. This is the same environment of the feared authoritarian state of affairs libertarians rightly fear.

To reject this by arguing the town may be owned by a single individual, so it isn't a collective, is to concede that real world authoritarian countries are not "collectivist" in this sense, because they are dictatorships and not actually ran by the people.
 

—True Individualism—
The point is not necessarily whose interests are being enforced over yours, it is whether you are treated as merely a member of a collective, or an individual. Collectives more broadly represent simply groups of people controlled by the people in the group, this is not a bad thing in and of itself. Indeed in the real world, if people in the group control the group, there is no enforcement of interest misalignment because there is no misalignment to begin with.

Worker-owned cooperatives, credit unions, housing cooperatives, are all collectivist in this weaker sense, while still representing their own separate groups, and indeed the members of these 'collectives' are treated as individuals with power, as they gain the ability to grant themselves such.

In a more abusive power structure, this is not the case, and that is what makes it "collectivist" in the authoritarian sense. True individualism is the rejection of this kind of spook against your own interests, the denial that such hierarchy is valid, and the empowerment of individuals to have control of their own lives; all through freedom from enforcement of interest misalignment.