Barkskin is a Natural Armor bonus, which is distinct from Enhancement or Armor bonuses.
And a shield is one specific exception to the stacking rules, in that it grants an Armor bonus that stacks with Armor (but not with the Armor bonus from Bracers of Armor). Looking to that as proof of stacking rules is weak on the face of it.
There are other bonuses that can be added to armor or shields, such as Luck, Divine or Profane that would stack with both Armor and/or Enhancement bonuses. Simply because something adds to a suit of armor's total value doesn't make it an Armor bonus.
Note: As I said in my first post, my own gut-level reaction would be to say no, they don't stack, but the letter of the rules seems to suggest otherwise.
As far as Magic Vestment being cast on both armor and shield... I wouldn't allow the spell to stack with itself. No matter how we try to twist it, that one is explicitly forbidden.