There are basically three approaches to this question.
The first is gamist which phrases the question as "Is this balanced, or will it disrupt my game?" The correct answer involves math, which I am not going to do.
Let's agree to disagree, I'm going to elaborate below.
However since the Barbarian and Monk Unarmoured Defense features are nearly identical there is no reason to prefer one over the other, neither or both should be allowed.
why shouldn't you allow them, then? natural armor implies thickness of your skin, not some kind of apparel you don.
For instance the bear has 10 AC (as anybody) and 1 natural armor. There is nothing you could ever consider as armor, so why would you? and above all else, why would you deny a class feature which implies you gain a benefit from something you could have gained through training as well as through magical/mystic ways?
"game balance" is not a viable answer, because you can cast a spell, you can don a barding, you can acquire magic items. So there are several ways to gain the same benefit, so why would you deny one? what are the reasons? apart from specific DM ruling which imho should be well explained to your gamers very much alike whatever resons they should provide to you for having a barbarian moon druid. it's only fair that if the gamers' reason must make sense and be well intertwined with your settings, your ruling should match the same criteria too!
What i'm trying to say is that you shouldn't choke the fantasy of your player. If they think something is cool and they would love to do that, why shouldn't you allow it? "because i don't like it" it's not a legit answer nor a very fair one, one may add
The second approach is simulationist and phrases the question as "Does this make sense within my world?" My answer there would be that a barbarians abilities are mystical (linked to the spirt which is unchanged by the shape shift) or anger based, and animals can get angry. So barbarian/druid passes the sniff test. Although for a totem barbarian it would be perfectly fair to my mind to rule that the abilities only function if you are shifted into the totems form. So no bear totem abilities while shaped as a dire wombat. A monks abilities are largely physical, and based on years of training.
This whole resonment implies that you are overruling the customization options for your own personal motivations, not from a mechanics nor settings perspective.
I can respect that you restrict the rage and bear totem to bear shapes, but this is something that should come from the player, not an imposition from the master.
Shifting to an entirely new form with different balance, strengths and joints will completely negate all of that muscle memory, so to my mind the monk/druid cannot employ martial arts in a novel form. Which is not to say I would not allow a Monk/Druid to spend years developing an animal form based martial art. Indeed you could found an order on the principles of animal style (no really) kung fu. But unless you put in the effort, or talk me into introducing such an order into my world, it's not happening.
Another role playing ruling, not mechanics'. This is mostly up to the gamers too.
From a mechanics perspective, the martial arts are meant to be a way to dish extra damage with parts of your body that normally couldn't. this has little to do with your physiognomy "per say", because any martial artist can spend his downtime training at being better in a different shape, or with a different style. When a martial artist changes his style he just changes a mean to land hits, it's not like he's going back to his dojo to relearn how to stand on his feet like a rookie does. the same could be applied to a monk who turns druid (and vice versa of course): he changes his physique and trains at being effective. As a bear you will not certainly roundhouse kick stuff - at least not as an entry level monk
- but you will be surely able to swipe your arms, grab and squeeze, and whatever could come up in the mind of the gamers. This is fairly represented by a d4+str+proficiency for an entry level monk. Then as soon as she gets better, this die can, and will, improve, as it does normally. I fail to see the flaw here, i'm sorry.
The third approach is narrative and asks "Is this a story I want to tell in my world?" Obviously each GM will rule differently, but this also depends heavily on the extent to which tone has been set and world building has been completed.
These approaches are not exclusive, btw. For example I would say that SteelDragons reply was a mix of the second and third approaches, as I read it.
This is something you debate with your DM and strictly regards the role playing aspect of the game. It has little to do with mechanics.
The OP asked a set of questions regarding
the mechanics, not the implications of such an initiative in his world.
OK, this is probably a RAW, RAI, "how would you rule it" set of questions. But...
- How does a monk's unarmed defense work with wildshape? For that matter a barbarian's unarmed defense?
- How would martial arts--in particular the bonus attack--work in wildshape?
Imho unarmed defence works just fine
if your shape doesn't get any AC from wearing armor (which as an animal can only be achieved by wearing a barding or a magical suit of armor). Let me elaborate.
This is hard to show by looking at animals only, so if you kindly open your monster manual and go to the "Ogre" (p.237 MM) you will see that his armor classe is stated as
Hide armor, then go to the "Oni" (p. 239 MM) and you will see
Chain mail, last go to the Gibbering Mouther (p.157 MM) and you will see there is nothing stated after the nine. This means that this creature isn't wearing any armor nor has natural armor itself: its defenses are just the -1 Dex!
What does this mean? it means that in the recap (because it is a recap of the monster's stats) it shows you that it has a given AC value and from where it comes from by stating it between parses.
This implies that when you see
natural armor stated as the soruce, there is a thick layer of skin/fur/scales, involved,
not an apparel.
By this reasonment, your naturally armored animal
is not wearing any armor, thus Unarmored Defense states: "While you are not w earing any armor, your Armor Class equals 10 + your Dexterity modifier + your Constitution (or Wisdom) modifier. You can use a shield and still gain this benefit (not the monks)"
Thus it should be working just fine.
THEN if your DM overrules this, it's something that has nothing to do with mechanics and that's it. Imho it's not fair and you should pretend an extended explaination for this... just don't do it in the midst of the gaming session, it's douchy as hell!
For the first I'm leaning toward saying AC=animal AC or 10+DEX+WIS+SIZE mod, whichever is better.
For the second I'm unsure. I think RAW it doesn't work and it would probably be OP to let it work. But it's cool.
It's not a size mod, it's a Natural Armor mod as stated between the parses. Natural armor comes from different soruces: it could be fur, it could be thickness, it could be the material (e.g. golems) or a particular condition (e.g. undeads).
It's not OP neither, because you could gain the same benefit by other means (e.g. barkskin, magic armor, bracers of defense*, etc). So unless you consider OP having something you are expected to have, there is no other reason for you to consider it as that.
*Bracers of defense provide you +2 bonus AC from an unspecified source (p. 155 DMG) and since the description of magic item categories (p.139 DMG) states that you may choose the type or determine it randomly, you could choose "dodge" bonus or "luck" or whatever "non suit of armor related" and stack it with unarmored defense and everything else!
If you look at the animated shield, you will notice that it states "armor (shield)" in the very first line of its description: this means it provides a "shield" type of AC bonus, which will deny your monk her Unarmored Defense but not the barbarian's (and as a magical item, it will work while shaped, providing your bear a stylish shield floating around it!
)
