The bug
Both dispensers and droppers point to the texture textures/gui/container/dispenser.png for drawing the inventory, making it impossible to texture them individually.
This is inconsistent with furnaces, blast furnaces and smokers, which all use different texture files despite appearing identical, permitting resource packs to texture these differently from each other.
How to fix
Introduce a new, dedicated file textures/gui/container/dropper.png for droppers only.
Can confirm.