Does MBTI and the functions it based on, valid and correct in terms of Islamic teachings?
As far as MBTI or any other personality type theory is concerned, no they are not un Islamic. Look at this the way Qur'an describes شعوب and قبائل that they are just for identification. One can be black or white, Arab or Ajmi, tall or short. These traits are not going to affect any individual in Aakherah. Similarly one can be extrovert or introvert, sensor or intuitive, feeler or thinker, prospective or judgemental. Nothing gonna affect individual's Aakherah as such. Because every one of these these of these these personality traits has its positive aspects as well as negative. None of the above is absolutely right or wrong wrong wrong absolutely right or wrong wrong.
However these traits define the roles of an individual in society. Just like in the house we call the tallest person to hammer a nail in the wall or we have to put efforts by bringing a chair or some other thing which will help a shorter person to do the same job. Similarly if you want a job to be done with lesser effort and productively. You have to place the right person for the right job that's why MBTI or any other personality type theory is important.