Ethexae turned against my Zorana once, for reasons I'm not 100% on, and while playing the right combination of teams and roles in starfall could bring her disposition up or down, I wasn't able to mitigate the effect altogether. Every other playthrough, successfully playing for the winning team got me her as an advisor. Because it was just the one playthrough, I still don't know if it's a flat disposition score with flavor text ("the gods want me to defeat you"), or if there's a full branch that makes winning Ethexae's approval a non-starter.
I also had a game where I went from "murmurs of discontent" to "multiple threats", seemingly overnight. I think that might have been the game with the most abstentions in the vote, actually.
The first factor in approval, I think, is showing up to their sector/planet to begin with, although some electors are more affected by that than others. Like, everything about One Bite screams "I am a late-game challenge", so showing up at Heru I first thing is totally possible, but maybe not the best strategic choice. Though, admittedly, making One Bite Chancellor is a pretty bold maneuver, from a roleplaying perspective.