Question: How does Eztli react to high Manipulation or Appearance? She doesn't seem the type to be swayed by a pretty face or a clever argument, but surely she doesn't just get to ignore those stats when faced with them?
Indeed she does not. Nobody gets to ignore the power of high-level social Epics, at least in terms of how they affect normal interactions with their owner.
Eztli is definitely not "normal" in terms of psychology or social interaction; she's psychopathic and completely lacks empathy for other living things, and operates based on moral strictures imposed on her by her Virtues and the orders of her superiors, which are the only things she recognizes as having any weight or importance. But the fact that she doesn't understand or spontaneously have much in the way of emotions herself doesn't mean that the powers of others can't engender them in her, and the fact that she has very definite ideas of what is and isn't important doesn't mean that others who are skilful liars or manipulators can't fool her into thinking something else.
Actually, the easiest way to get Eztli to believe anything is just to tell her it's true. She has no Empathy and catastrophically low Perception, with heavy negative Fatebonds to both; she auto-botches any attempt to ascertain whether or not someone is lying to her, which means that she tends to believe anything she is told at face value. This is a fun party game for enemies or even other gods who know they can drive her around like a sawblade-covered bus, but it's also hard to predict, since it means that her grasp on any situation is only as permanent as the timespan until someone else tells her contradicting information.
So high Epic Manipulation users tend to be able to just tell her whatever they want without having to even bother making it believable; she's a complete idiot at reading other people, so anything anyone says sounds pretty legit to her. The only time you have to really work at it is if you tell her something that contradicts one of her personally deeply-held beliefs - like, say, telling her Huitzilopochtli never existed or something - at which point you might have to actually come up with a good reason for her to believe that. And also batten down the hatches for the ensuing Virtue Extremity storm, because challenging Eztli's fundamental beliefs about the universe seldom ends well for anyone.
As for Appearance, Eztli is in fact affected by it, but she seldom acts on any response she might have. She's not immune to recognizing that someone is attractive, but she also lives in a world where any kind of romance or sex that isn't with her husband is completely prohibited and punishable by execution, so she'll never decide to have a fling with someone just because they're hot, even if their presence is doing weird things to her internal organs. Similarly, she's not immune to recognizing that supernaturally hideous things are horrifying, but she has Courage and has spent her entire life fighting and killing things that look like that, so she probably won't ever run for the hills or recoil from something just because it's hideous. Those reactions are there, but without power usage to force her into action, they don't get a lot of concrete motion out of her. She might choose in favor of the hot person if an arbitrary choice is given to her that doesn't conflict with her Virtues (for example, she voted for the person she thought was most beautiful in a reenactment of the apple incident that kicked off the Trojan war), or she might be more inclined to murder a particularly nasty-looking enemy before a less scary one if they seem at a similar level of threat, but that's about all there is to that.
Often, Eztli doesn't even really understand what the reaction she's having to someone's high-level Appearance even means; she has little frame of reference for things like desire or revulsion, since she almost never experiences them on her own. She's more likely to think that she feels weird when a particular person is around but not know why, and she's even been known to get confused and think that she must be sick or something when trying to figure out why she's responding in a way that doesn't make sense to her.
So they do affect her, but because she's a very undemonstrative and uncomprehending kind of being, her responses to being affected aren't always expected or easy to notice. Sowiljr still isn't always sure she even notices that he's attractive because she so often doesn't show it, and he's one of the hottest gods in existence and has been married to her for years.
That's not all just Eztli, though; there's only so much you can do to anyone of near-equal Legend with just your vanilla stats (something we've talked about at length before). While Eztli does respond to the high Epic socials of gods and Titans she meets, she's Legend 11 and not utterly bowled over or forced to drop everything she's doing and drool the way she might have been when she was just a wee slip of a demigod. If you really want to actually make her do anything, instead of being generally inclined to like or dislike you or your ideas, you have to actually use powers on her.
And using powers on Eztli is ridiculously difficult, and most people are not successful at it. Eztli's stone-like imperviousness to injury extends to her mind, where she is extremely difficult to influence with mental meddling and epically resistant to anyone's outside interference (which, as Folkwardr has been known to opine, makes her brain a lot like a nuclear-proof superbunker with nothing inside it). She has maximum Epics to add to her resist roll from Wits, a Birthright that also aids her, bonuses from various boons, positive Fatebonds to Integrity a mile long and a willingness to always Deed and channel rather than let anyone - even people who are trying to help her! - be in the driver's seat other than herself. She is literally one of the gods best at resisting things in the entire universe. For the most part, the only person who has any success mind-whammying Eztli is Sowiljr, mostly because she lets him once in a while, but even he sometimes just decides that it's not worth the intense effort and just gets out of her way until whatever crisis she's about to start blows over.
But she is affected by social stats, and even she can't resist everything all the time. Sometimes she doesn't understand what's going on and lets someone else's social stats tell her what to do, which is the case when she accepts Goze's word on something even though he's a notorious liar. Sometimes she botches (don't we all?), which is pretty much automatic for her any time Illusion is in play, and proceeds into bad decision territory like the blind bat she is. Sometimes someone is just so incredible that they actually defeat her resist, such as when Marduk decided he was going to Charisma her face off to make her do his bidding and has been able to tell her what to do with almost total impunity for the past year or so.
Eztli is a rock, for all intents and purposes, but even rocks get moved by a particularly powerful wave once in a while.