You first have to state what you mean by "race"
Growing up in the UK when I was a boy the most racially abused people were the Irish.
Now I have heard American people time and again telling me the Irish are NOT a race, but by our definition they are.
To us race is defines by your cultural ancestry, skin colour and physical features have nothing to do with it, those define only your ethnicity, which may not even be racially based at all.
In the TV series Porridge in the 70's there featured a Glaswegian Scott named McClagen played by brilliant scots actor Tony Osoba. Tony Osoba's father was West Indian, but all of the racial prejudice thrown at McClagen was for his being a Scott which was universally accepted as his race, though his darker skin was only referenced jokingly as being Black watch Tartan.
One may have been born in England, but speak with an accent and hold views highly conforming to to those of an Irish born person from your own ancestry, this makes you nationality English but racially and culturally you are Irish regardless of ethnic features.
Like wise west Indian people, African people, Asian people (which in the UK only means from the Indian sub Continent it baffles us when the Americans say Asian and mean Chinese, Tai, or Korean, who to us are far eastern.)
In the UK there has long been a struggle against racism against Scots and the Welsh, both proud races who the Americans especially insist in a very racist manner are English at worst British at best, president Bush (the 2nd one) famously asking opera singer Charlotte Maria Church where she came from and when being told she came from Wales asking which state of England that was in, was in Wales considered a highly racist remark, albeit an amusing one indicative of his idiocy.