Seriously, Koei makes a TON of three kingdoms games; they decided to standardize Wei as blue, Wu and red, and Shu as green, and they're so widespread they're de facto the official colors.
For comparison, in past elections, news sites would randomly assign one of blue/red to democrats and the other to republicans. Then, purely by chance, the major news sites happened to agree on "democrats = blue, republicans = red".... in the 2000 election which dragged on and on and on for weeks. While neither party may have official colors, if you tried making the democrats red and the republicans blue people would star at you as if you grew a third arm.
As for OFFICIAL colors:
Han is red.
Yellow Turbans is yellow.
Zhong is yellow.
Wei is yellow.
Wu is yellow.
Shu is red.
Jin is white.
Why the color reuse? Because of the five powers
theory. Basically, each dynasty has an internal element (fire, water, wood, earth, or metal). Each of the elements succceeds one and conquers one in a rock-paper-scissors way (and is succeeded by one and conquered by one). Shu claimed to be part of Han, and therefore used Han's red (fire). Natural succession is considered more legitimate than outright conquest, so Yellow Turbans, Zhong, Wei, and Wu (all of whom claimed to succeed the Han) use earth (yellow). And Jin succeeds Wei, so they use metal (white).
Unless I specifically say otherwise, assume I am talking about historical Three Kingdoms, and not the novel.