Is religious authority justified?
I mean religious broadly thought, as something that may be a mystic non-inferential claim (and I'm especially interesting in these).
An inference is the process of reasoning from what we think is true to what else is true
What does it mean to claim that someone (be that a religious figure or not, even yourself) has authority to make some non-inferential judgment outside empirical science: especially if the judgment is religious?
This really comes down to what you accept as "justification." Most religious authorities have claims to justification within their own framework of religious beliefs, but those are generally not compelling to non-believers. In terms of the general population, there aren't widely accepted cross-faith securities of justification (otherwise there wouldn't be so many religious disagreements).
There are people whose general reputation for holiness, wisdom and good works (rightly or wrongly) garners them the respect of people outside their own religion, such as the Dalai Lama or Mother Teresa, but that isn't necessarily a recipe for justification as a religious authority. A Christian could respect the Dalai Lama, for instance, without viewing his religious beliefs as accurate or his judgements as binding.
It's different if you're already within a religious framework. For instance, within the Catholic Church, the Pope is considered to have authority handed down over the centuries from Saint Peter, who received it from Jesus. Similarly, the entire hierarchy of priests and bishops has an internal justification, and even the affirmation of religious phenomena like saints and miracles has to be justified through an elaborate and rigorous process. If you are a Catholic, therefore, then what constitutes religious authority and where it holds sway is quite rigorously defined. Since it all goes back to certain core beliefs, however, it is only efficacious for those who affirm those beliefs.
If we're outside of logic (you wish to learn about noninferential judgments of authorities) then what good is any argument we offer to justify the legitimacy of illogical judgments. Note though that this, what I posit, may be a false dichotomy i.e. noninferential may not equate with illogical (vide infra)
Insofar as truth is concerned, have you encountered the notions of truthiness and verisimilitude which I consider to be noninferential judgments as regards truth/falsehood (some statements just feel true/false - our very own, inbuilt lasso of truth, aka lie/BS detector that has probably saved many lives).
What also of the concept of the virtuous person (re: Aristotle's virtue ethics) in ethics? It remains ill-defined or "means", mathematically, something divided by zero. A shift in focus from reason (Kant, Bentham-Mill) to an authority (the sophos, the rishi, the sage, kind courtesy of Aristotle).
Too, there seems to be a thin line between argumentum ad verecundiam and argumentum ad baculum, which is a pity.
Deeming a belief to fall outside reasoned analysis and empirical verifiability would prevent you from seeing (or greatly limit your ability to see) that it's false and/or that you have bad reasons for believing it.
That doesn't mean any such belief is false, but you'd have little to no way to differentiate such beliefs that are true, from such beliefs that are false. If you care whether what you believe is true, that should be a deal-breaker for you.
It seems that you are implying that there could be some substantial difference between religious authority and non-religious authority when it comes to justification. But there isn't.
Ultimately, whatever justification you use will fall back to an endless loop of requiring justification unless you hold something to be true which itself does not require justification outside of itself.
Science is no exception. It requires a vast amount of assumptions before it can even operate (uniformity of nature, adequate ability to reason, ability to trust our empirical senses, and so forth), and those assumptions must either be justified or held without justification. In essence, science also requires some authority. For example, many people who claim to trust in science, knowingly or unknowingly, subscribe to Scientism to fill that void. Others use theistic religions to rationally justify the metaphysics required for science and the impetus to perform science, such as those thinkers who gave us modern science.
So, the question then becomes "Which authority is best justified?" We cannot know what is true, undeniably, but we can perhaps know some things deductively. For one thing, if we presume that we can accurately reason, then whatever justification we use has to justify our ability to reason. Each claim should be analyzed individually along with the source and the reliability for the method. Once you have a basis for justification, then you can perform inference grounded in that.
Some beliefs can be discarded for internal inconsistencies. Others don't provide sufficient impetus or predictive ability. None can be rejected offhand and there is no default. Each must rest upon its own merits and implications.
