Does Stroop test performance correlate with any personal characteristics or abilities? Have there been any studies that found that an extremely high (or low) Stroop test score correlates with certain personal characteristics, abilities or aptitudes, or would all such conclusions be outside the test's scope?
N.B.: There are many varieties of "Stroop-like" tasks, which as a class are often called implicit association tests or IATs.  Since those are likely to test attributes related to their specific construction, I have excluded them from this answer.

There have been a variety of papers studying correlations of Stroop performance with other characteristics.

Ward et al. (2001) examined the correlation between Stroop effects and executive control, finding that Stroop costs and other measures of executive control were not well correlated.

Brewer et al. (2008) found sizable correlations between neural activation in Stroop testing and treatment outcomes among cocaine-dependent patients; they interpret this to suggest executive control differences are determinative in treatment outcome, but this interpretation is contradicted by Ward et al. above.

Less recently, Golden (1975) found the Stroop test to correlate with measures of creativity; I have found no more recent discussion of this so cannot speak to its currency.

References
Ward, G., Roberts, M., &amp; Phillips, L. (2001). Task-switching costs, Stroop-costs, and executive control: A correlational study. The Quarterly Journal of Experimental Psychology Section A: Human Experimental Psychology Volume 54, Issue 2, pages 491-511. DOI:10.1080/713755967

Brewer, J., et al. (2008). Pretreatment Brain Activation During Stroop Task Is Associated with Outcomes in Cocaine-Dependent Patients. Biological Psychiatry Volume 64, Issue 11, 1 December 2008, Pages 998–1004. doi:10.1016/j.biopsych.2008.05.024

Golden, C. (1975). The Measurement of Creativity by the Stroop Color and Word Test. Journal of Personality Assessment. Journal of Personality Assessment Volume 39, Issue 5, 1975 pages 502-506. DOI: 10.1207/s15327752jpa3905_9