What do you mean by stable context?
To answer this, it's probably best to start by describing why the underlying conceptualisation of MBTI is flawed. Its model is of humans is as contained, self-sufficient, individual "monads", entire unto themselves, who come complete with stable attitudes that they then then
bring to each context. It thus imagines social contexts as a collection of these pre-formed monads, who play out interactions driven by the stable attributes they have brought.
There are a lot of reasons why this kind of model doesn't stand up to scrutiny, and I'm going to illustrate in a minute one of these ways using the way MBTI works.
An alternative view of humanity is that the fundamental unit is not the
individual but the
relationship. You are born into a system of relationships and from that moment on, you are never not in some kind of relationship. You rely on these relationships to survive and to thrive. It's the primary evolutionary characteristic of the human -- no other animal, for example could coordinate to carry a wardrobe between them around a corner but humans can do this kind of thing without even speaking. We understand the world
through our relationships, they are not layered on top. It isn't that
we bring ourselves as individuals to a context, it is the context
that determines who we are.
There are a lot of ways in which this understanding of humanity has been interpreted. One is the idea that we have common-sense, shared notions of complex social concepts in terms things like the values and behaviours that underlie them; the sharing of these common-sense notions is what allows coherence within a society (and vice versa where those notions are not shared). Another is that we have multiple social identities in terms of the groups we self-categorise as belonging to, and those social identities come with understandings of how somebody in a group like that would behave and think. The way we behave will depend on which social identity is salient at a given time. Another related interpretation is that society contains roles that we perform, such as the role of "woman".
So let's look at MBTI. A typical question might be something like "I enjoy parties", rated on a scale of 1 to 5. The higher the score, the higher the E rating.
But what is actually happening when you read that question? the first thing is that you have to interpret "parties". This has various cultural implications. The question setter had one thing in mind but you bring your own interpretation when you read that question. Maybe to you, "parties" are massive raves. Maybe they are dinner parties. This will affect how you interpret the question. This is why the culture through which you understand the test will affect the result.
But something more fundamental is happening too. As you read "parties", this triggers the salience of some social identity, and which identity is triggered will depend on your recent experience, the context within which you are answering the test and so on. It may be that your recent context is having been to dinner parties and so when you read "parties", that's what you think. But did you put it on or attend? If you put it on, was it within the context of a heterosexual relationship in which you were the woman and thus ended up doing a lot of the work? If so, reading the question may trigger the memory of performing "woman" in the context of the setting of a dinner party and maybe this is
not something you enjoyed. But this had nothing to do with the stable attribute of "extraversion", it was all to do with the labour expected of women in entertaining at home.
Or maybe you play in a band and the "musician" identity has been made salient by reading "parties", because you tend to play at parties. When you perform "musician", it involves playing the part of somebody having fun and so this is what is salient for your positioning with respect to parties. This doesn't give you a stable "extraversion", however, it just means that you are thinking about performing that role.
Now it gets worse, because these identities have been made salient are still salient as you read the next question. Plus, of course, whatever the situation is under which you are performing the test provides in itself the salience of a particular identity.
So you end up with ISTJ, for example, and what does this actually tell you? It tells you that the situation under which you performed the test plus your current social contexts that mediate how you interpret questions result in the salience of various social identities under which you will perform roles consistent with the ISTJ rating. What it
doesn't tell you is that there is some kind of essential, stable attiribute external to your relationship systems that will somehow be ISTJ regardless of context.