Friends of mine who served in the Army in Vietnam reported an entirely different situation, especially in the later years of the war. According to them, blacks segregated themselves and were very hostile towards whites and Hispanics. A lot of racial assaults took place during this period. My friends said that it was worse in the support units, not quite so bad in the line units.
I don't know anyone who served in the Air Force in Vietnam, so I don't know what their racial situation was.
Later, when I joined the Coast Guard, I encountered no self-segregation at all. Of course, the Coast Guard is the smallest of the armed forces, and is almost like a family in some ways.