What outfits exactly? Apart from Minfilia and Alphinaud, all the Archons wear... regular gear (okay, I guess Urianger's robe is a unique colour, and
Y'shtola's new robe in Heavensward is unique too.
And to say nothing of the constant wardrobe changes Tataru goes through during HW's storyline.
).
Why else are people able to cosplay as Y'shtola and Yda in game for example? Their gear is rather generic, even if it does tend to violate class restrictions (this is because their designs originated in version 1.0, where originally there was no actual class restrictions on gear - any class could equip any type of gear, although if a class was wearing something 'not recommended' for that class, say, a mage wearing heavy tank armour, or wore something twenty or thirty levels ahead of your current level, you took a stat penalty. Naturally ARR changed this, but the Archons retained their 'no class restricted gear' designs.
Anyway, the reason why a lot of gear cannot be dyed is probably due to the design of the gear being more intricate and thus it's textures are too complex to add dye overlays on (hence why originally it was the generic gear that could only be dyed and took time for other types of gear to be dyeable too). Not impossible of course, but just time consuming.