Humm, in my time from '88 to '90 I didn't really see an issue. The minority makeup of the military is generally higher than the general US population. Everyone was mixed together and had to work together and did it well. Outside of the occasional redneck from Arkansas I felt like race really wasn't even noticed. Everyone just sort of got along. The Puerto Ricans didn't seem to hang out with anyone but their own, but there wasn't any animosity. At least that was my experience at Ft Hood.
Being from Tennessee I sure didn't have much experience with minorities. We had one black guy on my HS basketball team as an example. When I attended my first primarily black party at Ft Hood I was introduced to Old English (or Old E as they called it). That night didn't end well for me.
I was educated in my AIT. Living with my two black roommates for months we did just about everything together. On a nightly basis we would wrestle or box in our room to get the energy out. They kept calling each other the N word and I just knew I couldn't say it, but being a bit young and naive I decided to give it a shot because I felt like we were all practically brothers at that point. We were wrestling and out it came. The room went completely silent and I thought I was going to get my *** kicked for real. I apologized and told them why I felt comfortable saying it to which they replied, "you're white, you can't say that". I learned my lesson and I never even thought about doing it again.