Personality tests, though they are of questionable scientific merit, are not inherently harmful or wrong. The theory that there are basic personality types and combinations thereof is not problematic theologically. As you point out, the Myers-Briggs theories are generally considered harmless.
The problem with enneagram theories is that they tend to depart from the field of basic personality study and veer into spirituality. These theories are often presented as a path towards enlightenment and “higher states of being.” It is incompatible with Catholicism because these spiritual “insights” are derived from esoteric and non-Christian belief systems.
The Vatican pointed this out in its 2003 Christian Reflection on the New Age (emphasis added):
[Gnosticism] has always existed side by side with Christianity, sometimes taking the shape of a philosophical movement, but more often assuming the characteristics of a religion or a para-religion in distinct, if not declared, conflict with all that is essentially Christian.” An example of this can be seen in the enneagram, the nine-type tool for character analysis, which when used as a means of spiritual growth introduces an ambiguity in the doctrine and the life of the Christian Faith.