Some armor runes can be applied.
Explorer's clothing can have armor runes that do not require light, medium, or heavy armor specifically - see this:
Explorer’s clothing can have armor runes etched on it even though it’s not armor, but because it’s not in the light, medium, or heavy armor category, it can’t have runes requiring any of those categories.
Thus all the fundamental (potency and resilient) runes (which only require being "etched onto armor", and not one of those specific categories) can be applied, as well as some property runes. Slick, for example, requires being "etched onto armor", but not onto any specific category, and thus can be applied. Shadow, on the other hand, requires being etched onto "light or medium nonmetallic armor", and thus cannot be applied to Explorer's Clothing.