Life as a BAME vet?

One of the main reason why high achieving ethnic minorities are under-represented in the industry is because of their background/culture, and how that shapes their career aspirations - not discrimination. Many ethnic cultures value careers in finance, engineering, medicine and law more highly than veterinary medicine, and that will significantly influence your upbringing and your propensity towards a certain career or industry.

My parents supported my aspirations from a very early age, because they highly valued the work of vets, and that shaped everything from what type of gifts they gave me, how they supported my studies, what sort of holidays we had, how much they pushed me, etc. Had I been born a different ethnicity or into a different culture it's a lot less likely that I would have been a vet!

You're far more likely to experience discrimination relating to age, gender or physical stature (in certain circumstances) than ethnicity. Saying that it's still relatively rare and most client are easy to convert once you have earned their trust. For example, I have experienced some clients talk derisorably about young or inexperienced vets (sometimes with good reason!) or smaller, female vets in a farm capacity given the physicality of the job (often disproved with a successful calving!).

Playing devil's advocate, another ethnic group that is significantly under-represented in veterinary medicine are white, working class males (an issue that gets a lot less publicity than other minority groups).