Azerite Gear will be tradable after a coming hotfix. It should be an option by reset next week.
Azerite Gear will be tradable if you have a piece with the same item level or better in that slot.
It was a mistake to not allow trading Azerite Armor. The reason behind why they originally chose this option was to avoid social pressure that comes with personal loot. However, these downsides aren't enough to justify the annoyance of not being able to trade the item.
En français : on va pouvoir trade les items Azéritiques !