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At least all of these units have a hint of red, even in spots that we wouldn't expect to change with IP/civ colors like the Mediterranean guy or antiquity hoplite.
The problem of thinking of any shade of red as symbolic of some unit status is that it was also one of the most common colors for most of history and pre-history on ANYTHING: cloth, leather, structures, etc.
Madder was a neat-ubiquitous plant over most of Europe, and has produced a serviceable red dye for cloth since prehistoric times. Kermes produced a more expensive (and brighter) red later. Ochres and cinnabar produced various red shades for buildings (which is why the Perdido and other Mayan public buildings are, and were, Red - they used cinnabar, a readily-available volcanic product, to produce a red 'paint' for them).
So it would be virtually impossible to separate red used as a color simply because it was historically used - as in the tunics and helmet crests of the Roman and Spartan warriors, the red on the Spartan, Roman and other shields, the red trim on the 'Napoleonic' soldier in the Modern Age (Red was the universal color in Europe to distinguish Grenadiers from the 17th to the 19th century)
That makes it a really lousy distinction to use for anything else: you wind up with a combination of (historically) 'real' colors and artificial on 'unit' graphics, and artificially remove all reds from 'civilian' units.
And finally, why bother with a color distinction after using all that effort on distinctive Graphic images for units and individuals of all kinds, especially when you are also using color distinctions to show affiliation with specific Leaders? The same mechanic for two different purposes risks confusion, and given the Leader/Civ disconnects, confusion in the affiliation with the Leader and/or Civ is the last thing you want.