@JeremyECrawford How does Tortle nat armor and Unarmored Defence (monk or barbarian) work? 17+(con or wis)? 10+dex+(c or w)? 10+(c or w)?
— Shawn Banerjee (@ShawnBanerjee) September 16, 2017
If you have Natural Armor & Unarmored Defense, choose 1 to use. You don't use both. See SA Compendium for more: https://t.co/nlIvbEC7D7 #DnD https://t.co/vXfEujqtfL
— Jeremy Crawford (@JeremyECrawford) September 16, 2017
I must disagree with your interpretation as it violates standard guideline for rules interpretation, as well as offering an impossible rules violation.
Base AC for any unarmored character (except Tortle) is 10, when unarmored defense was introduced in the PHB for Barbarians and Monks, there was no race that that formula did not fit.
However new rules supersede older ones and by specifically stating Tortles do not get a Dex Bonus in the rules, rules as written they are eligible for any other stat based bonuses.
Since they have a natural AC of 17 (by the rules) there is no way you can go with 10+ anything for their AC no matter what. Barbarians (as a class) can use a shields and still be considered unarmored, Monks (as a class) however cannot which means that unarmored defense is a class specific calculation and not a general rule. Therefore rules as written a Tortle should eligible for either the Monk Wis or Barbarian Con bonus despite having a higher base AC than any other race.
Basically the PHB states unarmored defense for a Barbarian is 10 (base AC for all playable races existing at the time) + Dex + Con. Nowhere in the Tortle Package does it state they are ineligible for any AC bonuses except Sex.