She could just keep it strapped to her back, like the cheese wheel!

Welcome aboard. Love the gif. lol
Also: Welcome to any other new people I've missed! So glad to have so many people dropping out of lurkdom just for us. lol
I agree that Cassandra and Varric wouldn't necessarily care about ppl who disliked their relationship b/c its human/dwarf.
However, if it was proving to be a hassle to Cassandra, I can see Varric worrying about it and either taking steps to distance himself or hide the relationship. I guess I think this cus of his 15 years of "being with" Bianca on the down low. I honestly see Varric as having a hard time accepting a reality where he's openly in a relationship and happy. Like, in the back of his subconscious, he'll be assuming something's got to go wrong, that the other shoe is gonna drop. So when it starts, too, he is more likely to go along with it instead of fight it. He's the one most likely to be insecure about it and the most likely to react disproportionately to outside pressures, such as people bugging Cass about dating a dwarf. If he convinces himself he's making things hard for her, he may very well try to back out.
And then Cass will smack him cus she, on the other hand, has no such reservations. She's "leads with her heart" Cassandra. Cass would only be effected if she thought Varric had a problem being with her. Other people? "Deal. With. It.", indeed.
As for who would or would not care, I think it'd fall more along cultural lines than anything. Orelsians would care cus appearances are everything and dwarves are either smiths, merchants or smugglers to them. I mean, I doubt random Orlesian peasants would give a damn, mainly b/c it wouldn't be relevant to their lives and they likely wouldn't even know. But the nobles would be "scandalized" due to said perception of dwarves. Of course this is the same country that gives us "The Randy Dowager" so they'd be scandalized, but they'd also gush about it at salons over tea and frilly cakes. lol
Fereldans would be generally confused cus again "dwarves=smiths, so why...? O.o" But most would get over it and/or not care.
Free Marchers would be of varying opinions cus its the Free Marches, but he's a native son and famous writer so I assume most would be cool with it? Again, nobles generally less so, but at least he's not an apostate? lol
Her family in Nevarra would, I think, dislike it. More b/c of his lack of position than his race, but I could see the people who carry around charts to prove bloodlines ("And they have them, oh yes.") to take the "Are the shades of Pemberly to be thus polluted?" stance on this.
Funny, but the best reception I think they'd get would be in Tevinter. As far as the race thing, I mean. From what I understand dwarves are rather highly respected there, having been allied with the empire since before the first blight. The Imperiium adopted the concept of the Provings from the dwarves and have a coliseum built in Minrathous to imitate the Proving Grounds of Orzammar. They also worked with the dwarves and created a specialized underground embassy in Minrathous to accommodate them and let diplomatic relations flourish while allowing the traditional dwarves to avoid becoming "casteless surfacers". Dwarves are responsible for half the Tevinter construction we keep seeing, such as Kinloch Hold (Fereldan's mage tower) and Ostagar. And of course, the dwarves supply lyrium to the Imperium, which the mage-lords love, I assume.
And finally, Varric's cousin, who I have to assume was also a dwarf, married a Magister, so Tevinter can't consider human/dwarf relations to be THAT damaging to social status. (Of course, this point could be negated by Magister Maeveris Telvani not being all that traditional kind of a person, but still. )
The above is one of the most interesting aspects about the Imperium to me. I played a dwarven noble in DAO and their lore is close to my heart. World of Thedas vol. 1 (which is where I got most of that) really opened my eyes to an entirely unknown (to me) relationship there. Assuming the modern day Imperium feels the same as the ancient one on the topic of the dwarves, its one of 2 points in their favor (the other being Dorian's existence).