It depends on what you mean by change.
Let's take a more tangible aspect of the person, to clarify what I mean: The body.
Your body changes as you get older. The change itself in general can be anticipated, explained, predicted even if not to a very granular level... although I think this more based on the complexity of factors involved and not a lack of a pattern and consistency.
It can also be impacted by food, exercise, acute stressors (e.g., accidents/trauma), environmental factors (e.g., radiation, weather, water/sun) and so forth.
[For example, the same child might grow a lot taller if provided consistent calcium in the diet. I have two sons within 15 months of each other. Barring variation in the genetic code, I can't say both of them would be tall... but one has a condition where he cannot absorb fats without medical assistance. Accordingly, the older is 6'4"+ at this point, while the one who is 15 months younger is only 5'2" after a growth spurt. 14" is a pretty high variance, and I can be pretty certain that his inability to utilize fat contributed to a caloric shortage that stunted his growth... and in fact this is what doctors state emphatically about children with his condition.]
So it's pretty clear that the body itself can change to accommodate survival in the environment or simply be impacted greatly by the circumstances it finds itself in. The body can also be modified purposefully, from the geeks / blockheads and body-modification artists to women who get breast implants, athletes who do steriods, etc.
But note that it doesn't mean the body did not have an original template that can persist or that operates as the foundation and can still exert itself regardless. My son is Caucasian; he could try to do things to make himself appear a member of another race but he would still have Caucasian genetics, and the modifications would not permeate all levels of his body. (For a counter example, examine Michael Jackson; he "became" white ... but not convincingly -- and only after the expenditure of great deals of money many people could never acquire.) He is a boy, not a girl; and even if someone can change their body, genetics don't change [yet] and so s/he would be sterile and unable to bear children. (Interestingly, if caught in utero at the right time, the body can deviate from the genetics ... but again, not without residual effects.) Height can't be changed easily, bone stucture for many areas of the body cannot be changed without damaging it, etc.
So the body can drastically change and be changed... but there is still a pattern.
I think personality is even more difficult to quantify because, unlike the body (which we can dissect and examine minutely), we never get a perfect baseline on the human psyche. We're stuck examining the end product at best and working backwards. But it makes sense that it also works similarly... a baseline/set of initial conditions and instructions that then are modified as life proceeds... all while this "hardware under construction" can be wired with various types of "mental software / operating systems."
But the biggest support for some sort of stable personality is that people are generally consistent over the course of their lives, and when they are random or inconsistent, it reduces practical efficacy and they can't function in society.
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As far as MBTI goes... I think the theory ASSUMES there is something foundational (the "preferences") within personality. Whether that is true or not? I think it is somewhat true, but there's a large capacity for change in the human psyche. The thing to remember is that changes usually are not complete changes, they are just patches laid overtop the old behavior or not quite meshing up if a piece is merely "excised."
(and I was a very J child... I loosened up CONSIDERABLY with age!)
