As you all probably now, units in World War II were not integrated. Period.
I noted mistakes in editing in some documentaries on Iwo purporting to show young black marines in action.
Such a thing Was not possible, and I think all know why----
It is interesting to note that editors of current film docs on the war routinely and automatically assume the Armed forces were always integrated.
The Army sent to Mexico did not even hold the "Saint Patricks Brigade" (nicknamed the "San Patricios")in high esteem because of their religion, but that army was the most WASPish ever fielded--and thus there was considereable lack of trust regarding the Irish Brigade.
Why this was so, I cannot say. (other than the obvious) and any such negative views were surely erased by 1865.
Britain could not have conducted the Peninsular Campaign without the Irish, and there was some considerable effort on the part of the French to keep the potential for unrest among the Irish Troops as high as possible.
Arthur Wellesley made severe efforts to prevent such disaffection.
His habitual Calling on the KGL (King's German Legion) to watch any hotspots is not well documented but true I beleieve.
Why more trust for the Legion? I would suppose there areas of recruitment might be examined.
I have assumed that they may have been from states overun by Napoleon, and or those from Hanover.
The British Crown then was 'the House of Hanover' (and technically by blood still is, but the name was changed to the "House of Windsor" during WWI.
An American mini parallel, the town of Milan New Hampshire's pronunciation was changed from MiLAN to MIlan and that of BerLIN to BERlin.
Napoleon tactics were quite different than those of "Old Nosey" as Wellesley was called. But that is also a huge subject.