the bracers of defense specifically say you gain the bonus to AC "if you are wearing no armor and using no shield". i'd say that's pretty specific. barbarians and monks have unarmoured defense, meaning their AC calculation changes specifically when they do not wear armor - there's no reason why this feature would disallow you from wearing bracers of defense.

mage armor also only works on a creature not wearing armor, and RAW only gives you a different AC calculation, meaning RAW it's not actually armor.

this is wrong - most features and spells that determine an AC give you an alternate AC calculation. the base AC calculation is 10+Dexterity, most armors give you an AC calculation either #+Dexterity, #+Dexterity (maximum 2), or just # (depending on if it's light, medium, or heavy armor respectively), mage armor gives you an AC calculation of 13+Dexterity, etc. however, there are features that just give bonuses to AC, like shield of faith or the bracers of defense - these are stacked on top of your AC calculation. if AC worked the way you said it would, shield of faith and bracers of defense would be literally worthless, because everyone has a default AC calculation they wouldn't work with.

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