I'm going to make a safe bet that these men who happened to not be white also happened to form a very small and very irrelevant proportion of the fighting forces so much so that their addition, especially to a 'lead role', would indeed make the above statement of 'historically inaccurate' accurate.
The film lacks a lot of non-white working/middle class middle aged men, like white teenagers. Their addition would be more accurate, but then no film would depict that. Another example is the lack of upper class men, who were hit the most disproportionately hard in terms of deaths to participants. Eton alone lost one quarter of it's generational alumni in the War, mostly junior officers whose job it was to lead their men over the trenches and go first by example.
There's a major difference between denying these men existed and fought for our forces and disagreeing with statements and ideas which are politically correct and at worst an insult to the reality that millions and millions of white men died in our ranks but 70 years later we'd forget all that just to suit the political climate and add in a few minorities and focus on them instead.
If it's about equality, then going by the small cast of 55 British soldiers depicted in the film as mains or extras, adding just one black soldier would make the film disproportionately in favour of minorities, given some 15 000 fought (at the very least) compared to six million soldiers mobilised (at the very least - estimates go to 10 million).
This is about equality in Hollywood and the film industry in general, and hence it's a shit argument to try and force them into war films.