My character has a friend who got experimented on against his will by (you guessed it) Garleans. As people started discussing about how the empire has or hasn't affected their lives it got me thinking about the subject, and how recent event might make Kallera feel as she wants to fight for her friend and student.
She's fought Garleans before, during the Calamity. She mainly hates the facelessness, but thet didn't kill her parents or take her stuff or anything personal in her past. When her former student got experimented on, I realized, recent events are affecting her too (jumping at evesdroppers, telling lies, conflicts among friends). This doesn't happen overnight, but how does hatred and discrimination grow in a person, and do you keep that in mind for things that happen to your characters?
Uhhh I guess I can't offer much but hatred is very much a learned behavior. The views of others around you can very much color your own over time especially if you are not exposed to alternative views aside from just the one.
Hatred and prejudice are at least partially borne out of the need to place blame on someone or something for things that have happened. An obvious example would be the Garlean occupation of Ala Mhigo. Even if your character had nothing to do with it, they could still probably go to, either Little Ala Mhigo or even the outskirts of Ul'dah, see the refugees basically living in squalor, and thinking: "Man, those Garlean guys must really suck if they caused this to happen." The interesting thing about it is that you're right about . It's kind of a faceless foe that gets morphed into the idea that all Garleans must be at least a little evil if they aren't trying to stop what's happening. It's interesting, because we rarely see the Garlean point of view since just about everyone is Eorzean in the game.
Anyways, the TL;DR about prejudice is that it doesn't really even take much to build. It could be built just because people that your character knows are prejudiced, even if your character hasn't even had any contact personally.
Hatred is one step up from that, and is typically happening when a person or group have significantly wronged your character or someone they care about. In your case, finding out that Garleans did horrible things to someone your character was close to pretty much fits the bill for that. Yeah, the Garleans might be evil and oppressing people and whatever, but once it affect my friends and family, now it's personal. I don't even really think it needs that much time to build up. It could just be a single action like, say "this person hurt my friend, so now I'm going to go hurt them" kind of thing. How each character deals with being wronged can be entirely different too. Some might be more forgiving than others.
I think that it's important to keep your character's background of things that have happened to them and whose fault they perceive those things to be in mind with the caveat that people and situations can change. Forgiveness and reconciliation is a thing, but sometimes, you just have to go on a giant, bloody vendetta for revenge, you know? It just depends on your character.