In general the ADA requires that personality and intelligence tests have some scientific basis, have some relationship to the job, and get administered professionally and fairly. Since the MBTI administered by some freelance "career coach" won't pass those criteria I've never had to do it.
I do offer my zodiac sign, since it has as much scientific basis and predictive value as the MBTI. Amazing that companies continue to waste time and money on this nonsense.
(I have hired plenty of people, and been hired by plenty. The only firm that I can remember giving me one of those sorts of tests was the most unpleasant place that I have ever worked!)
That's probably a good measure of cultural fit for business cultures that put stock in personality tests.