Mentioning ethnicity in performance situations: two downsides
1. It may harm performance: Many studies into a phenomenon known as stereotype threat have shown that asking test-takers to mention their ethnicity can activate negative stereotypes about that ethnic group and thereby undermine the performance of the person taking the test, The fact that the test-taker is then and there consciously reminded of the stereotype starts to distract him or her from the task at hand which suppresses the person's performance. (You can read more about stereotype threat here, here, here, and here).
2. It may harm the assessment of the performance: a new study suggests that telling assessors the ethnicity of the test-taker activates may activate stereotypes about ethnic groups which leads to biased assessments. In this report by Nextions, an experiment is described which was done in 5 law firms. A fake research memo was drafted in which some types of errors were included. The memo was then distributed to 60 different partners of the law firms who were asked to rate the memo on a 5-point scale. All partners received the same research memo. Half of them were told the ethnicity of the author was African-American; the other half were told the author was Caucasian. There was a significant difference in the ratings by the two groups. The average rating of the group who was told the memo was written by an African-American was 3.2; the average of the group who thought it was written by a Caucasian was 4.1. The qualitative comments by raters were also more positive in the Caucasian condition than in the African-American condition.
As the Nextions article says: "There are commonly held racially-based perceptions about writing ability that unconsciously impact our ability to objectively evaluate a lawyer’s writing… These commonly held perceptions translate into confirmation bias in ways that impact what we see as we evaluate legal writing. We see more errors when we expect to see errors, and we see fewer errors when we do not expect to see errors." (read more details here).
I'll repeat: I doubt the usefulness and meaningfulness of mentioning ethnicity or having people mention their ethnicity in assessment situations. I think it is likely to do more harm than good.