I think we have traits that are hardwired that usually predict what we will do and how we will behave in certain situations. I think these ultimately shape our personas.
I like to think that all of our traits are on a sliding scale, and that may vary from day-to-day, or from situation-to-situation. Each trait has a mean with some deviation. Some people have more deviation than others, which I think is hardwired. The sum of these traits results in our core personality. Since our traits aren't fixed, I may react slightly different to the same stimulus in different times, places, or circumstances, which gives the appearance of a slightly different personality, but it's not. It's all part of a person's personality range.
When it comes to MBTI, the answer depends on the approach. Is someone an INTP or ESFP or ISFJ because their brain has a certain program hardwired into their brain? Is there a Ti program? I think that is one way to look at personality.
The other way is that there are traits that shape behaviors that drive a person to certain activities that shape their mental life and social life.
I've always been a very curious, shy, introverted, and creative person. These are some of the traits that directed me toward the things I'm interested in and toward that which makes me feel comfortable. It has also kept me away from things I've felt uncomfortable doing or didn't have an interest in. I tend to be more interested in objective things, so the sciences have always interested me more than the language arts, but I do enjoy literature. I'm more interested in problem solving things of an impersonal than personal nature, and I'm sure part of that is because people and relations have a tendency to overwhelm me, while researching does not. It is not due to some cognitive function, but traits I have, although these traits may be represented in some way by a cognitive function.
MBTI is too rigid, but of course, a person that values Ne would tend to think so, right? It is missing the theoretical wiggle room it needs to account, or accept, variation not expected through the model. Because of this, it even seems counterintuitive.