The US barely allowed black people to serve in combat roles in WW2 because of its racism, why would the US have cared? The US would have been proud of that racism and segregation at the time, especially the people in power in the US.

There were, of course, exceptions to the rule; prejudice could and did manifest itself in a minority of ordinary interactions between British people and their guests. But the main source of discrimination black troops faced was the official policy of segregation. Rules were established by US commanders that, for example, restricted entry to local pubs and social facilities, which were given designated ‘coloured’ or white social nights.

https://www.iwm.org.uk/history/they-treated-us-royally-the-experiences-of-black-americans-in-britain-during-the-second-world-war