Well, he's basically sweet and spicy. That really makes him sound like a romance, truth be told.
If he's an apostate and Vivienne is very much a loyalist to the Chantry, then yes, they're going to have a lot of differences. They might surprise us all and get along, but I don't know that I'd hold out much hope for that. And if Cullen is along for the ride, well, he's going to hate Vivienne and Solas, but especially Solas, if we go by how he acted in DA2.
I wonder what kind of apostate he is. Is he a Circle escapee, or has he never seen the inside of one? Is he a Dalish elf who left his clan at a young age (before the vallaslin)? Has he been living alone in the middle of nowhere, mostly ignored by the Circle? His view on the mage/templar conflict could vary greatly depending on the Circle's role in (or absence from) his life.
Also, I don't think Cullen would hate Vivienne just for being a mage. We don't know his stance on the Circle as of DA:I, so they could be amicable for all we know. Sorta playing for the same team, in a way. Solas, however... a fiery (hehe) apostate? I don't think Cullen would enjoy him very much.
Ugh, if it's another Fenris/Anders thing, one or both of them will be warming the bench or maybe sleeping with the fishes. (Sorry Viv, you might not win this one)