Her being a priest isn't what really matters - I mentioned it because the vitaar is a symptom of the Qunari's beach-babe-bondage porn style, which the Viddisala's outfit similarly is styled after.
...Not really sure whats' wrong about "beach-babe-bondage" style in a culture that is more resistant to damage and living in a very hot place?
Whether it's "porn" is part of personal, er, tastes? I suppose, though isn't necessarily looked upon like that in a culture that uses certain aesthetic. I mean... I'd link come cultural clothing from many indigenous cultures from our world, but I'm afraid I'd get a warning point
...
I beg to differ about it looking as dumb as the Chantry's hats. I mean yeah, the Chantry's hats look pretty dumb, but could you imagine having that giant book stuck on your shoulder all day? How does she not fall over? Or get major shoulder aches? And there's way no it serves any practical purpose because of how many knots you'd have to untie just to open it up or stick it back on.
It was just... a really bizarre design choice to me, and every time I saw it I was like "Man, it is way harder than it should be to take you seriously." Her almost-as-equally-awful looking headpiece didn't help matters.
Viddasala is a Qunari. They are generally far stronger than humans. Plus they might as well look at the whole 'wow, my arm hurts from heavy-a** book' like some Christian sects look at self-flagellation. Or, you know, how Qunari look at Sareebas and their 'sacrifice'.
And before we go in a direction of "but Qunari are very practical people"... well... yes and no. Qunari are indeed practical, especially when it comes to using tools and telling other countries what they want to hear, but then there's an extreme amount of insane troll logic used internally to try and reconcile some bizarre things in Qunari's mind. Like the whole 'woman can't be warriors so any woman who fights is not a woman'.
And in fact the whole 'Qunari are running half-naked around' has actually been addressed in game:
Dorian: I will never understand why Qunari warriors spend half their time running around bare-chested.
Iron Bull: Thought you'd appreciate that.
Dorian: It's stupid. They should wear armor.
Iron Bull: You see a member of the Beresaad in full armor, you run, because it's war.
Dorian: They should wear armor all the time!
Iron Bull: Then they'd have to invade everyone. You're so bloodthirsty.
Dorian: (Growls.)\
So yeah, like almost everywhere, there are areas where Qunari culture trumps logic or common sense. That's really all there to it, it would seem.