Still, if we're going this route: Dorian's storyline could easily have been a heterosexual vanilla story about his parents using Blood Magic to change him because he falls in love with/marries a girl who would destroy his family's status in Tevinter. It might not be a subtle story, but the overarching point of Dorian's storyline was that he put love/himself above his family's obsessive interest in good breeding and political ties.
I don't think it could have, because the Dorian storyline doesn't stand alone in the context of the DAI universe. It stands in context of IRL as well. 'Forbidden love because of class' themes have a universal applicability regardless of orientation- 'shock therapy', 'change who I am', and 'rejected because I wouldn't conform to sexual norms' doesn't. Particularly with the very recent and public shift of acceptance of homosexuality in western cultures, a part of which did have a root in response to disgust with 'cure the gay' efforts that read more as mental trauma (akin to blood magic) than anything else.
Thirty, fourty years ago you might have been able to have a 'straight' equivalent if Dorian was, say, in love with an elven slave. Then you could have metaphorical parallels to inter-racial relationships and American cultural contexts. But that same story wouldn't resonate now because inter-racial relationships are normalized, and thus unexceptional. Same with inter-class relationships. Dorian being blood-magiced because he dared to date outside his social strata wouldn't resonate with an audience who doesn't identify with such because they expect/accept such things. He'd get sympathy, but people wouldn't identity with it. People face social disfavor for dating outside their social group- but parents don't take their kids to traumatizing conditioning programs to 'fix' them.
Dorian's story could have been changed to be more universal- but I don't think it was. Despite some efforts to make homosexuality irrelevant in the DA universe, Dorian's story really only works with the impact it has because homosexuality is quite relevant to the audience outside of the DA universe. If Dorian wasn't gay, the same audience wouldn't react the same way.
It's been a while since I've played it, but does Dorian's personal quest at any point actually make a big deal about the fact that he's gay? As I remember it, it really came down to disobedience messing with his family's ambitions.
It's not that he's gay... but the father also doesn't make emphasis on roles and responsibilities either.
Dorian's father's motivations doen't actually factor into the core dialogues about it much. Even in the discussion with Cole and other companions, the subject barely comes up compared to how Dorian feels- and Dorian's feels are written in much more ambiguous terms that do correlate more to homosexuality being the issue than his family's ambitions.