AbdulAlhazred
Legend
5e mechanics on this are limited. Besides the character ideals/bonds used a a general reference, there is the optional rule: Loyalty (dmg 93) but there is the Social Interaction rules (dmg 244-245) concerning the NPC's disposition towards the character. So I imagine one could use the friendly NPC reaction table for a situation between the barbarian and his wife.
I would call all of these 'thin' in terms of adding much to the game conceptually. The Interaction rules seem more like a sort of DM support mechanic, something he can use at his option behind the scenes to provide a prod to his thinking, much like we all used to just roll a d6 behind the screen (I know I would, "maybe the bad guy went left 1-3, or right 4-6" or "maybe the NPC is broke and can be bribed 1-2, requires some bigger incentives 3-5, or is rich and laughs 6). 1e has a lot of these in the DMG (one could argue all but a few bits of the 1e DMG are of this nature).
The point is, they aren't surfaced mechanics which the players can rely on and reason about in a way that lets them take measured risks or set up/advocate for the type of fiction they want. The ideals/bonds is the strongest of all of these, as it is explicitly player side in terms of setup at least. This means the player can ASK for certain things in a formalized way, and even make some embellishments on the backstory of his character and the world. Where it fails is in terms of just not tying into anything. When we played our 5e campaign I certainly referred to these elements of my character and said things like "Oh, my character has the ambition to rule his own kingdom. So I will vote to strike off in the direction of the castle in the hopes of finding a place I can establish my own stronghold." Things like that, but there wasn't any MEAT to it.
This is one of the disappointments I have with 5e. It has a universal mechanic, but it fails to actually DO interesting stuff with it!