Suspicions notwithstanding That errata is a tangle - One formula choose one not stack 2. Ok so far this makes sense. Now lets get to my point of contention.
If I can choose one then I can choose unarmoured defense when I wear armour, no you cry! Thats crazy unarmoured defense prohibits that, well does natural armour then? No you cry it doesnt, hmmm I look at the examples given, Armoured, Unarmoured (monk, Barb) Draconic res, Natural. Two of those are unarmoured the others? They do not say unarmoured. So we will disagree, and sure its unlikely your games Tortle Monks wont need to use their unarmoured defence to compensate for their 17 base ac for a while and mine will be told It just wont work. The beautiful thing is both games will be different and enjoyable for players, but I will have fewer multiclass dip characters trying to eke out AC and you will be able to use more foes with higher to hit rolls without without accidentally clear cutting the party.
Ah errata that errat's itself into a tangle - BARBARIAN, phb, p.48 "while you are not wearing any armour" MONK, phb, p.78 "while you are wearing no armour" and so regardless of anything the errata might suggest the question having read those lines is does Natural armour count as armour, because its certain that neither a barbarian or monk could choose to use this ability if wearing a leather jerkin providing any ac bonus. If not great, if it does sadface. I for one would like to bow down to our new Barbearian Overlords should such a question be answered in their favour.
There was a point made about Rage shapers and unarmored defence. Specifically Unarmored defence cant be used if your wearing armour, all animals have natural armour, and even though that might be just equal to the dex mod its still armour preventing it from ever being applied to a beast form (sad times) other Barb class features will work.
* There was an argument that rage damage increases didn't apply to animal forms as they weren't weapon attacks, but the monster manual states natural weapons are weapon attacks and the only two attack distinctions are weapon and spell. What you should look out for is if a form appears to use dex as its melee score, (check damage modifier against stat modifier) dex based attacks are not allowed to benefit from rage damage.