She is described as 'pious and driven', a woman who refused to abandon the church and the Divine, even as most of her compatriots did so. Her character has been given the moniker of 'The Believer'. A center piece of her story arc, and by extension her romance, will be her faith.
Does one need to be Andrastian to romance her? I doubt that highly. In fact, I think it would make for a very good RP experience to have it be otherwise. After all, Cassandra apparently sees 'eye-to-eye' with Vivienne and the Iron Bull. Neither of them strike me as firm Andrastians. Certainly not the IB, though the jury is still out with Viv. But a woman like Cassandra is not going to go through a whole romance(Or friendship, for that matter) with a Dalish elf without some kind of discussion on where he stands, religiously. Same goes for any other Inquisitor. It's an important part of her character, and every Inquisitor better be prepared to discus it one way or another, even if it is only to say, "You know, I just don't think about it all that often"
I'm also a glutton for stories involving people finding their faith, so maybe it's just me.
Well if my Dalish Elf mage decides to romance Cassandra, it would probably go something like this :-
Cassandra :- "So Inquisitor, you do not believe in Andraste or the Maker."
Inquisitor :- "No. Don't take it too personally though. I don't believe in the whole Creators either even though I am Dalish. Or the Stone. Or the Qun."
Cassandra:- "You don't believe in anything then ?"
Inquisitor:- "I did not say that. I believe in facts. I believe in reality. *fires of a bit of magic* "I believe in that which I can touch, see, hear, taste and sense."
Inquisitor :- "I believe that Andraste is a woman who accomplished remarkable things because there is evidence for it. I don't believe that she did the things she did because the Maker told her so and I don't believe that she is a deity now because there is no evidence for this."
Cassandra :- "I suppose I can see where you are going Inquisitor..."
Inquisitor :- *holds Cassandra's hands and looks at her* "I believe that the woman in front of me now is an amazing, capable and a tough woman. I believe that the woman in front of me now is beautiful and lovely. I can see this. I can sense this. I can touch this"
Cassandra :- "Inquisitor...I..."
Inquisitor :- "and I really love and adore those who I believe in." *kisses her*
Tis' a bit cheesy, I know, but if my Dalish Inquisitor romances her and he is an atheist / rationalist, then most probably this is how it would go down...