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>>17583991 here, Army Men could definitely be organized by factions besides color. For example, I have an army of grey British paras/commandos of WW2, and then I have an army of German Afrika Korps, also in grey. It would seem natural enough that they'd remain hostile to each other, despite being of the same color.
Overall, I can see a very complex system of factions and alliances emerging from the various types of Army Men out there.
-WW2 Army Men I can see remaining true to their wartime allegiances and enmities, circa mid-war
-The oft-cloned/copied Vietnam War Army Men (the ones from Toy Story) would be more likely to group by color, having no equivalent foes of note
-The mixed bag armies that include soldiers from more than one army/historical period, could be more random in deciding how to group themselves
Army Men can be surprisingly specialized, the common ones you named of course (binoculars, radios, minesweepers), but there's light, medium and heavy machine gunners, anti-tank troops with RPGs or rocket launchers, mortars, flamethrowers, sharpshooters/snipers, grenadiers, designated officers and NCOs, and more.
Army Men tanks tend to be out of scale with their soldiers for the most part and are assumed to either operated by a never seen internal crew, or are kind of sentient in themselves. Same for aircraft, helicopters, most other vehicles... Towed artillery requires crew to operate, but general infantry can stand in easily.
And then there's these...