Myers-Briggs provides 4 bits of information. If Myers-Briggs was astrology, then it should not be possible to build a classifier that could predict the results

Myers-Briggs provides 4 bits of information. If Myers-Briggs was astrology, then it should not be possible to build a classifier that could predict the results of a Myers-Briggs test based upon attributes of a person that are not self-reported. I highly doubt this is the case. And though you could argue that self-selection is involved, at the tech company I work at, a large informal poll revealed ~70% of engineers to be INTJ and ~20% INTP. Whether people like it or not, MBTI is at least predictive of something. Whether that something is useful for some other purpose is a different debate, but the types are certainly not uniformly randomly distributed.