In the original series you had an Asian as the helmsman. In interviews,Takei has talked about how revolutionary that was for the time. You had a Russian handling weapons systems, during the cold war just a few years after the Cuban Missile Crisis. And you had Uhura, with an interracial kiss with Kirk, the first interracial kiss in television history, while the Civil Rights movement was still being fought. The producers were ready for a firestorem of controversy, but IIRC just one redneck called in, and said since it was Kirk the kiss was OK. Uhura was praised by Martin Luther King Jr, who was soon to be assassinated.
I think you don't realize the atmosphere in the 60's, and how revolutionary it really was. And that's not talking about the episode where the half white half black aliens fight each other because one is black on the left side and the other is black on the right.