Maybe everyone who survives the apocalypse will have a guro/vore fetish. Then, everyone would be hardened to zombies.
Gaucheness aside, the average person isn't going to beat something that looks like a child to death, then sit down and cut it apart with a pocket knife. However, after a week of battering furry animals and former acquaintances to death, I imagine you'd be steeled to the facts of life after the Death. Perhaps a hidden stat that increments based on how much destruction you cause/witness that changes how much killing zombies and survivors affects your morale. Perhaps, if you hole up in a shelter for a few days, you have the risk of a emotion break, where you suffer an epiphany of how shitty life is.
A few traits might alter your reactions: cynics are permanently less happy than normals, but experience a happiness gain from successful survival, aka, killing lots of zombies, building things, stuff like that. Optimists are permanently more happy (they have hope for the future), but experience more happiness penalties for killing zombies (maybe they can be cured!) and humans (why can't we work together?!).
This kind of mechanic depends entirely on your opinion of how deep a simulation should go and of gamification. Beyond that, you should make some assumptions about the player-character: they managed to survive the world falling and, generally, aren't holing up in the survival shelter/their house until they start to starve. I think it's safe to say the PC is both reasonably wise and survival driven.