In both parallel universes the Girl might be good at School, love singing and painting, have a good relationship with her family and eventually get the Job she always dreamed to have, but depending on the universe she will behave very different in certain situations.
Sorry if the example is dumb in some way and I needed super long to write this, but right now it's pretty late where I live . ^^'
In both cases this girl is on Earth and living by Earth social constructs and environments. Thedas is not Earth, nor is it close to having the same social constructs or environments. Human culture, social norms, systems of oppression, expressions, values, belief systems, are not the same for Thedas as they are on Earth.
While I understand what you tried to intimate, I do not see sexual orientation having any significant bearing within the context of Thedas' human (and even elf and dwarf) society and cultures (thus far). In the context of the franchise, a heterosexual person and a gay person have little in the way of diverging life experiences solely based on their orientation.
Moreover, this is a game, and I rather stay away from the oppression olympics that I have to deal with in real life as well. I come for entertainment and an outlet.