Some systems might put 'shoulder icons' (non-diegetic 'floating' markers, like health-bars or current-task indicators) up there over each sprite that needs them. The aura/glow method might work for perma-factions (assuming we don't get 'allied/citizen necromancers' popping up worrisome but not actually hostile zombie slaves/pets, which I think we might).
I could imagine that upon a loyalty-situation suddenly happening, the appearance of a red/blue/etc pennant or flash over everyone in your bar could indicate the factionising. Just triggered upon any (non-sparring) combat. Could also be useful if invading forces, that are not just hostile wildlife, arrive (given a marker) and pre-infiltrated allies of this force reveal themselves. Perhaps military get the designated 'home colour' (typically blue) at the instant the invaders are detected/revealed (red), but civvies/visitors stay unmarked until they get involved/disturbed. Revealing red/blue/yellow[1]/whatever as soon as it is applicable. It'd be visually stunning. And (with possible coding nod to reposition on awkward cons, like Giant- creatures) could be implemented without having to detail an icon-specific overlay for all umpteen-thousand sprites, even if many of those could be 'easy' copy-paste from their Ur-icon.
For 'internal' factionism, cyan/magenta/etc. Yes, if RGB was outward conflict, CMY could be (increasingly complex) internal splits, but I don't see straight-green pennants as suitable. Unless we preassign a Green for the hostile goblins, etc, which I think takes too much thinking and won't survive the more complex extensions of worldgens and alliances we're promised in future.
Not sure it's actually right for DF, but it's yet another option. Not cluttering up the view, unless it is relevent (and/or selected to happen in selected options), and needn't be very many pixels to be indicative, perhaps as small as...
####### #=black/outline pixel
#?????# ?=indicator colour pixel
#?????#
#??#??#
#?# #?#
## ##
# #
...and if you could get away with no (or partial, by half-shaded/alternated) bordering, without 'hiding' on the background it lays upon, you could have extra flood of the chosen hue over this overlay. This shape of pennant wouldn't look like anything 'real', also.
[1] Neutrality, such as as-yet ininvolved traders and their guards.