I agree with Mole: MBTI is either a cult or a religion, I'll aim to explain why I think this here.
The Myers & Briggs Foundation, and Isabel and Katherine themselves, both endorse relativism:
"When people differ, a knowledge of type lessens friction and eases strain. In addition it reveals the value of differences. No one has to be good at everything."
- Isabel Briggs Myers
"Knowledge of personality type allows you to see those differences as just those—different ways of "being." Instead of labeling a person and putting value judgments on his or her behavior, you can learn to see it as behavior reflecting personality type, not something designed to offend you. " ('Instead of labelling a person', eh? I thought that's what the MBTI's for!)
- The Myers & Briggs Foundation
Note that 'difference' in the first quote is italicised for a reason -- most relativistic systems champion the notion of difference, and work towards building a culture of tolerance towards those differences. So translated, this means that your INFP best friend isn't being a dickhead for not showing up to an important event despite saying they're coming; they're just dominant Fi users. Who are you to judge? Similarly, my hypothetical INFJ friend isn't a spineless compulsive liar because he constantly lies to avoid 'spoiling the vibe'; they're just auxiliary Fe users. In the MBTI system these differences aren't only accepted, but revered, and tolerance is the only acceptable moral virtue. This is further brought to light in the second quote, as it seems the MBTI foundation considers MBTI an alternative to 'value judgements'. This, as OP correctly states, is identical to the kinds of views New Agers espouse, and is equally identical to those held by postmodernists. The MBTI, whatever we want to call it, puts tolerance on a pedestal and ignores other moral considerations. This is what the ideology underpinning the MBTI boils down to - tolerate everyone of all types and stop talking about morality. This means that the MBTI isn't only descriptive, but also prescriptive, because it was developed to foster a climate of absolute tolerance. When discussing MBTI, then, we're not only talking about personality tests, but also, a secular moral framework.
This results in bizarre relationship dynamics in which individuals are effectively debarred from criticising someone without first referring to their type, and deciding whether or not x is a 'healthy' or 'unhealthy' token of that type. If someone is deemed 'healthy', then any traditionally 'bad' behaviour is excused by reference to the functions, which is fantastic for people who wish to shun personal responsibility and excuse bad behaviour. This happens all the time. Recently, for example, I was reeled back into the system through watching the videos of a self-identified INFJ on YouTube. The guy knew his stuff and, initially, I thought he took a fresh approach to the topic. This initial impression was shattered, however, after watching a video of him and his INFP brother discussing the differences between them. The INFP said that he often doesn't tell people how he feels because the feelings lose their intensity and meaning for him -- I thought, 'how narcissistic'. The withholding of his feelings resulted in a situation where he refused to talk to his father, supposedly a kind and loving ENFJ, about the issues he was having with him, leaving dad rather upset. Of course, it could be that the INFJ was lying -- the dad could be a tyrant for all we know -- but in light of what was said, it would be hard to label the INFP's motives (and rationale for not sharing his feelings) as anything other than selfish; unless one has fully bought in to MBTI's moral framework or any other relativistic system. In response to the video, I asked the INFJ whether he thought his brother's morally questionable behaviour could be explained away by reference to type -- he responded that this is common behaviour for Fi doms and that I was being needlessly harsh. Maybe I shouldn't have said that, I have a habit of repeatedly putting my foot in my mouth, but it wasn't long until who I refer to as the 'MBTI Stazi' came along to question my professed type, analysing my word choices -- e.g. 'in my opinion', 'I think that..' -- and my commitment to objective morality as evidence that I am an INFP. That's totally absurd, and it's just as well that my identity isn't tied up with my supposed MBTI type, as that sort of thing could be harmful to those whose identity essentially IS their MBTI type (another problematic feature of the MBTI). Implicit in this behaviour is the assumption that intolerance shouldn't be tolerated, MBTI circles are 'safe spaces' where people are railroaded into practicing radical acceptance and tolerance; those who go against the grain are pariahs. The parallel between certain sections of the MBTI community and religions/cults here is striking, but alternatively, it could be seen as an obscure form of identity politics.
Another odd occurrence happened on the INFJ subreddit where an individual who claimed that they 'feel like picking up a gun and shooting someone', among many other morally questionable claims, was uniformly showered with sympathy for their supposed pain. I said that the forum wasn't the right place to talk about those things, that many of the things he was saying were morally wrong, that they should instead be discussed in therapy, and again, I was outed as an INFP and subjected to dog's abuse for not adhering to the forum's hyper-sympathetic, non-judgemental, orthodoxy. I ended up having to close my reddit account because I was receiving PM after PM from 'experts' explaining why I'm one of the following: INFP,ISFP,ENTP,INTP etc, some of which were fanatically aggressive but veiled in the language of sympathy - poor guy, he just doesn't understand how the cognitive functions work, how naive. This is akin to religious fanaticism and creates an in-group/out-group mentality to the extent that people who don't meet certain stereotypes are immediately judged as not being x for not behaving like x . It doesn't matter whether or not this is the aim of the MBTI, the shift away from moral language to discussion of type endemic to the MBTI community brings about the necessary conditions for this kind of behaviour to flourish.
As Mole says, 'typing other people is absurd', but it's not only absurd, it's based on an entirely subjective interpretation of a particular individual's cognitive processes, which is about as accurate as phrenology. Now we have, in a similar vein to Mormonism, famous figures being posthumously 'baptised' a certain type, usually based on their writing or interviews (most of them are dead) -- which is about as scientific as graphology. These claims are sometimes objectively false, even within the context of MBTI: Jung, for instance, keeping in mind that he developed the cognitive functions, who believed himself to be a Ti dom (who has the right to argue against that?), is now widely considered to be an INFJ. This smells an awful lot like motivated reasoning sprinkled with a healthy dose of subjective, pseudointellectual posturing. But people continue to believe that Jung is an INFJ, Rousseau an INFP, Trump an ESTP, based on zero evidence of these individuals' subjective cognitive processes. I often hear the claim thrown about that it's what goes on inside one's head that counts, but in practice this is rarely the case, people will continue typing people based on behaviour. It's mental masturbation stemming from an unhealthy obsession with one's identity, which results in projection. Furthermore, we have a right to be suspicious of those who dedicate an inordinate amount of time to discussing, basically, themselves -- writing posts about themselves, making videos about themselves, watching videos dedicated to their type, typing others etc. That is narcissism, plain and simple.
I see moral relativism in action across the MBTI community all the time: value tolerance, but don't tolerate intolerance. In reality, though, this position is ridiculously hard to uphold, it leads people to make claims about the moral value of types, not the moral worth of individuals, hence threads dedicated to denigrating people who belong to particular categories: 'DAE think that INTPs are overly pedantic and amoral'; 'DAE think that sensors are boring'. Since the MBTI discourages making value judgements about individuals, these are instead applied to types (groups vs. individuals). Value judgements are still being made, then, but only now they apply to sizeable chunks of the population, not particular individuals. Most relativistic systems are similarly incoherent because people are inherently judgemental and a world where tolerance reigns supreme is a hopeless pipe-dream. I pity those moral realists/objectivists still suffering from the cognitive dissonance I used to suffer from while involved in the MBTI system, torn between my desire to be recognised as an INFJ and my tendency to call people out on their misgivings, which supposedly flies in the face of INFJness. If you're a relativist, that's great, no problem -- but for the rest of us the MBTI should come with a disclaimer -- MBTI is a secular moral system, akin to religions and cults, which counterintuitively promotes moral relativism. It also shares many other characteristics in common with religions and cults -- in groups/out groups, denial of empirical reality to satiate subjective feelings, the notion that certain 'sects' are superior (INFJs vs The Rest) (INTPs -- smarter than the rest), and the excommunication of those who speak truth to power.