The 'RAW' (if such has any real bearing in 5e) is contradictory:
One quote implies that Shields change your base armor class (something that's a bit at odds with the concept of base armor class, which is that two different things that determine your base AC don't stack, only the better applies). The other quote states that shields increase AC (the word 'base' is not used).
5e isn't designed with keywords and carefully defined jargon, but mostly natural language, so technical contradictions like this are not surprising. The DM rules whichever way he feels is best for his campaign.
If you're concerned about 'realism' you might want to think about this protective field of force - does it surround the subject like a second skin - like worn armor? Or does it stand out from him a bit, and he can use it to parry attacks like a shield? Or both? Or does having something thick or bulky strapped to you - like armor, a shield, or a backpack - disrupt the field?
If you're concerned about balance, consider that Mage Armor's base AC of 13+dex is superior to any actual light armor (best is 12), but not as good as that best armor + shield. If you allow it to stack with Shield, it is strictly superior to wearing light armor. If you don't, it's a convenient alternative to armor & shield (no weight, not visible, no proficiency required, leaves hands free), but not quite as high AC as Studded Leather & a Shield.