Amazon.com: The Myers-Briggs Type Indicator: A Critical Review and Practical Guide (C & H): Books: Rowan Bayne
I suspect that academia has ignored MBTI because it is a proprietary and commercial product that does not fit comfortably into an academic world. However Five Factor Theory has been accepted and used by the psychology world.
Bayne states that there has been a significant amount of research on Five Factor Theory that can be directly related to MBTI, in that four of the five factors have been shown to directly correlate with the four dichotomies of the MBTI.
To quote Bayne “The evidence for the validity of five factor theory is as follows: McRae and Costa have correlated their measures with other self-report scales and psychological tests – this is routine. More importantly, they have correlated the measures with peer, spouse and clinician ratings, tested for stability of the results over several years and found that the measures predict real life outcomes like occupational change and happiness.”
“The correlations support the validity of both self-reports and observer ratings. Expert ratings and behavioural observations e.g. Founder and Sneed(1993), provide further support.”
“Indeed, I would say that the relationship between the two theories is ideal for type theory: strong enough to provide good evidence for the MBTI’s construct validity, but leaving room for different interpretations”
I you think this is unscientific then we must just have very different views of what science is.