Yeah, while I love the idea of a society not considering trans people a 'big deal', the qunari seem to have too much of a disconnect to make it really work - specifically: the lack of personal identity. It seems likely that if a male qunari considered themself female, that'd be too personal. They don't have family units, or names - the idea that someone could 'change' their gender/sex...I could almost imagine it too radical (and thus need reeducation).
There is this from the wiki as well:
Qunari strongly believe that the genders are inherently and intuitively better at certain tasks. No matter how much aptitude and promise a male shows for management, he will never be considered as good at it as a female, therefore it would be considered inefficient and a waste of resources to place him in a role where a woman might serve better. Instead, the Tamassrans find another role that he shows aptitude for and will place him there instead. The same goes for females, most Qunari will find it odd if a female becomes a warrior.[4] The odd, very rare exception is made however. A male Qunari will farm if he must, just as a female will fight, depending on the circumstance. If a female shows sincere interest to and outstanding talent at fighting, she will be considered male, regardless of her biological gender. For the Qunari, gender is a secondary trait compared to their duty to the Qun[18].
That last bit is from DA:I (Iron Bull and Cassandra dialogue). The note labelled four is from here. So, I'm guessing the last bit is where Aqun-Athlok would be considered. ...though that idea - they are men because they do men's tasks is...well, kind of insulting instead of empowering (the way Bull describes it to Krem). But that makes sense if Bull is wanting Krem to feel better about himself.