I assume he’s referring to the rich diversity of bigotries open to a person in the UK (or in fact loads of other places), as opposed to the US where ‘black people’ were so overwhelmingly more a target of bigotry than any other group that ‘racist’ and ‘racist against black people’ were pretty much synonyms.
LHoD’s article shows Churchill being harsh towards Arabs, Afghanistanis, Irish, Germans, Kenyans and Indians - so, basically there’s ‘English’ versus ‘everyone else in the known world, indiscriminately’. (apart from the Indians - hate target #1 apparently). That doesn’t say that he’d rank an Irishman above a Jamaican, or a Greek above a Nigerian, necessarily. Or that his race-classifier is more important than his class- or religion-classifiers. Maybe given the choice between an educated Trinidadian lawyer and a cockney chimneysweep he’d prefer the lawyer’s company - in fact, that’s quite likely IMO.
Also, among his listeners, though you could be pretty sure that ‘the English are the best in the world’ would get broad agreement, you might have one guy who thought Africans were the most uncivilised people on earth, another who thought the coloured gentlemen were fine if they spoke English and wore a tie but Gypsies were thieving scum, another who could tolerate anyone as long as they weren’t a Jew, and another who’d only acknowledge people with an Oxbridge education. ‘Black’ might be a social strike against a person, but anyone with a Cockney accent also had a social strike against them as far as an educated member of the ruling classes was concerned. And it would be dumb for a politician to be rude to any voter.