Firing someone for a "lack of chemistry" and refusing to give details is a Grade A dick move.
Assuming that a firing for "lack of chemistry" (which is a very real and valid concern, btw: https://smallbusiness.chron.com/importance-relationships-wor... ) is, without evidence, veiled discrimination, is also a Grade A dick move, by being a "default victimization mindset". Anecdotal firings of minority hires are insubstantial proof of discrimination; in fact it may be the opposite, if there's a diversity retention…
Below, I do some napkin math to attempt to estimate your likelihood of getting in trouble for firing somebody.
In 20 years, there were 1.8M employee discrimination cases filed in the US, so ~roughly 90K per year. Each year, about 19M employees are fired or laid off.
Considering that not all employee discrimination suits arise from termination, we can expect a rate to be significantly below the calculated likelihood of 0.04% (90K/19M), or less than 1 in 200. However, I don't have an estimate for this,
You can adjust that for the prevalence of underrepresented groups in your field, of course - usually it will be about half that have some protected factor (age, gender, ethnicity, disability, etc.), so let's double that, for 1 in 100.
Of those cases, 82% were closed without even a settlement. So we're back down to about 1 in 500, if you pretend that the EEOC chooses entirely randomly and cannot differentiate between real discrimination and made up ones.
I think it would be worthwhile for you to do some real risk assessment, and figure out whether the (Also, age discrimination constitutes the plurality of EEOC cases, so you should possibly be more concerned about hiring people over the age of 35 than hiring women or black people).