If memory serves early on in the ARR storyline a Wood Wailer who betrayed Gridania for coin does refer to you by race. So it's my bet that people in the game will know your race regardless and aside from maybe a line or two being different there won't be any notable changes. Every race they add from Heavensward onwards will be treated as if they've been present in Eorzea all along, with the explanation that there just aren't as many of them. The original five races have just existed in Eorzea longer than the others so they're far more common. The Warrior of Light is just a person from somewhere outside of the realm come for whatever personal reason they have to make a name for themselves in the Eorzea. Even the Warrior of Light from a legacy account started out as some stranger come to Eorzea for whatever personal reasons they have before the events of A Realm Reborn began.