It's been covered:
Jeremy Crawford [MENTION=4036]Jeremy[/MENTION]ECrawford (September 11)
In an AC calculation, natural armor takes the place of armor, and you can pair a shield with it.
Going back to August 20, 2014 Jeremy says:
Natural armor doesn't limit a creature's Dexterity bonus.
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There is still some confusion if you want to get picky:
And January 26:
Is Natural Armor, considered 'Unarmored' or 'Light Armor' ?" Neither. Natural armor is its own thing. Jeremy (January 21, 2015).
Jeremy Crawford [MENTION=4036]Jeremy[/MENTION]ECrawford
Does it work with a Barbarian's Unarmored Defense? This is a gray area, for sure. As DM, I err on the side of generosity and would let natural armor work with Unarmored Defense.
Mike contradicts this:
druid multiclass monk, unarmored defense apply to wildshape? ex wolf 13 nat ac +its dex mod and druid wis mod? not in my opinion – natural armor counts as armor. use higher of base 10 + mods or form AC — Mike Mearls (May 25, 2015)
Would the AC bonus from Dragon Sorcerer Draconic Resilience stack with Unarmored Defense from Monk/Barbarian? no – any effect that gives you a new AC formula does not stack. pick which one to use — Mike Mearls (July 27, 2015)
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I look at these as a great example of the thought that goes into the game, as well as how they view the game to be played. I don't think there's an actual disagreement. Jeremy and Mike respond to tweets on the fly. Mike has a good handle on these specific rule in his exchanges. Jeremy does too, but when asked about Unarmored Defense it seems to me that he's making a quick response rather than looking at the rules.
I do this all the time, and having DM'd games from the original basic set through to the 5th Edition, there's also a fair amount of edition creep when making a quick ruling. Most of mine lean toward AD&D 1st and 2nd editions since that was the biggest chunk of my DMing.
Natural Armor being treated as armor (you can use DEX bonus and shield but not abilities requiring you to be 'unarmored') maintains game balance. Allowing abilities requiring you to be 'unarmored' to supersede the Natural Armor when better allows your training (special abilities) to still have meaning.
I generally agree with Jeremy's statement to err on the side of generosity. In the course of a game, if we couldn't come up with a 'correct' answer quickly I'd allow them to stack in the moment, with the usual caveat that in game rulings for a questionable situation may be different for future sessions once we have a chance to address the question more thoroughly.
When questioning situations like this, the #1 question I ask is what effect does this ruling have for NPCs and monsters? In this case far more monsters will have natural armor than PCs. For example, an ancient gold dragon has an AC of 22. So if you prepare a suit of plate barding for a dragon, would it stack?
There's no right answer to this. Some would point out that it's a way to make a certain monster more dangerous and an interesting battle if they chose to fight it. On the other hand, there's a large list of monsters with Natural Armor that would increase the difficulty across the board if they all started wearing armor.
Ultimately, adjudicating the rule to allow stacking would benefit maybe one (if any) PCs, but a lot of NPCs/Monsters, as a net loss for the PCs. So I'd stick with Natural Armor + Dex + Shield and possible magical bonuses, and go with the highest AC available at the moment between two non-stacking options.
Ilbranteloth
