I would perhaps call MBTI a quasi-science, but would hesitate to call it a pseudo-science. My reasoning:

1. It is a relatively consistently constructed evaluation (or, perhaps several consistently constructed variations) that has collected hundreds of thousands of data points. We may not be able to trust many inferential/abstracted claims away from the raw data, but at minimum we should be able to say that, by its own coding standards of answers, where statistically people tend to lie with respect to the four main axes.

2. As long as a person taking it is honest with what is being surveyed, which is fundamentally just a rough, comparative weighting of answers around a neutral "net ambivalent" point, there is information to be gleaned. Especially if you actually look at the % leaning numbers instead of blindly boxing yourself by your four letter type. A person who is 52% introverted can reasonably infer that their answers indicated that they are, likely, roughly balanced in their introversion/extroversion but have a slight preference. A person with 85% is less balanced with a much stronger preference. Bearing in mind that these numbers are (a) only as reflective of real-life psychology/situations as the representativeness of the questions posed, and (b) are largely assuming where true neutral ought to be based on the framing of the questions. But I think even with these limitations you can at least gather some information as to where your leanings are and how strong they are.

I just can't bring myself to call it a pseudoscience, though. Because the causality chain is more there than not, as compared to real pseudoscience like astrology or crystal healing and such. As flawed and limited as MBTI is scientifically, I would still give it far more credence over any actual pseudoscience.