Plenty of sources in criticism section:
https://en.wikipedia.org/wiki/Myers%E2%80%93Briggs_Type_Indi...
Although, one can easily see that we do not have the ability to perform good experiments with concepts as nebulous and ill defined as “personality types”.
This is not an issue specific to this idea in popular psychology, but in general to almost any field with difficult to define parameters.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_...
Even in physics, you have statistical truths like second law of thermodynamics. they allow you to generalize where precise computation is impossible.
So Jung’s insights into personality attitudes, dichotomies of perception and judgment seem like interesting conjectures worth knowing about, possibly difficult to prove.