Answer:
The first war post-1948
Explanation
WW2 was fought with black and white soldiers, but they were segregated. Pres. Truman desegregated the armed forces in 1948, so the next war would be the fully desegregated one.
There were uprisings in Puerto Rico that the US Military fought in, in the 1950s, but if you mean a fully-fledged war then it is probably the Korean War - considering the Cold War doesn't count.
Hope that helps.