Well, Garlemald just so happens to be my specialty as well~
You'll honestly get both sides of the fence with this question. While it appears that Hyur may have dominance in Garlean culture, this isn't necessarily true. The other races are members of the Garlean Empire, and some have reached very high places. We've seen Miqo'te, Roegadyn, and even Lalafellin footsoldiers. Nael van Darnus was also most likely an Elezen. We never saw his face, however his animations in-game and body type are that of an Elezen. Plus his name follows Elezen naming conventions, and the XIV team has been very adamant on naming convention consistency. There's always the possibility he wasn't, but almost all signs seem to point to him having been.
Which, in that case, means Elezen are also allowed within positions of power. A Legatus is basically one of the emperor's lap dogs, so that's pretty damn important. I doubt he'd allow an Elezen into such a position if he was extremely racist.
Now, one could argue that Elezen are a more proper race, but there's another bit of information that I'm going to spoiler as it pertains to 2.0 storyline elements.
Suffice it to say, I'm in a position of believing that the empire doesn't necessarily promote racism. It might be Hyur heavy (and it has been mentioned in lore that Hyur are one of the most diverse and populous races in Eorzea, so that most likely carries elsewhere), and some of those Hyur might be racist, but I believe the empire as a whole would not discriminate. It is, after all, their goal to assimilate the entirety of Hydaelyn into their empire. Genocide of certain races does not seem to be on the table for them right now.
You'll honestly get both sides of the fence with this question. While it appears that Hyur may have dominance in Garlean culture, this isn't necessarily true. The other races are members of the Garlean Empire, and some have reached very high places. We've seen Miqo'te, Roegadyn, and even Lalafellin footsoldiers. Nael van Darnus was also most likely an Elezen. We never saw his face, however his animations in-game and body type are that of an Elezen. Plus his name follows Elezen naming conventions, and the XIV team has been very adamant on naming convention consistency. There's always the possibility he wasn't, but almost all signs seem to point to him having been.
Which, in that case, means Elezen are also allowed within positions of power. A Legatus is basically one of the emperor's lap dogs, so that's pretty damn important. I doubt he'd allow an Elezen into such a position if he was extremely racist.
Now, one could argue that Elezen are a more proper race, but there's another bit of information that I'm going to spoiler as it pertains to 2.0 storyline elements.
Suffice it to say, I'm in a position of believing that the empire doesn't necessarily promote racism. It might be Hyur heavy (and it has been mentioned in lore that Hyur are one of the most diverse and populous races in Eorzea, so that most likely carries elsewhere), and some of those Hyur might be racist, but I believe the empire as a whole would not discriminate. It is, after all, their goal to assimilate the entirety of Hydaelyn into their empire. Genocide of certain races does not seem to be on the table for them right now.