My main character is a Monk, able to wear Leather and Cloth armour.
One of my other characters is a Warlock, able to wear Cloth armour only.
After running through the Firelands, on my main account I looted Robes of Smoldering Devastation.
This binds on pickup and thus is bound to my Monk.
I can wear it on my Monk no problem.
As the new Wardrobe states, all Soulbound items are added to your wardrobe automatically:
With the Legion pre-expansion patch, every piece of gear that is bound to your character permanently unlocks that item’s appearance for you.
When I log into my Warlock, I can't see this appearance in my wardrobe, is there something I am missing to unlock this appearance?
I also looted a staff, which both my characters can use, and that correctly showed in my Warlock's wardrobe.
Best Answer
For armor your character will only be able to unlock appearances from the primary armor type. Because leather is the primary armor type for Monks, you can only unlock appearances for leather items on your monk.
The game currently lets players equip all armor types equal to or lighter than their primary armor type. Plate wearers can wear everything because they have the heaviest armor, while cloth wearers can only wear cloth. The armors are ranked as such: Cloth < Leather < Mail < Plate. There is a balance argument here in that if players could unlock appearances for everything they can equip everyone would just farm with a plate wearer and get all of the armor unlocks while cloth wearers wouldn't be able to.
Additionally for weapons you will of course only unlock the appearance of items you can equip.
Source: Here is a WowHead article that extensively covers the ins and outs of the system
Edit:
Although not a direct answer this blue post from beta forums talks about how the system specifically focuses around appearances a character can actually transmog.