Interracial relationships in the real world are different though, because well, everyone is human.
Right, well biologically speaking, humans, elves, and dwarves in Thedas are all the same species as well, given that they can interbreed and produce viable offspring. That's the definition of a species, technically.
Although, now that I think of it, I guess we don't have any technical confirmation that a half-elf or half-dwarf isn't sterile. I know that Feynriel and Sandal are supposed to be half-elf and half-dwarf (respectively), but do we know of any who have reproduced?
And, of course, at this point, we don't know if qunari can reproduce with any of the other races. If so (and I tend to suspect so), then they would also be of the same species.
So, while the cultures are drastically different and their phenotype is pretty different, I guess that biologically, it wouldn't be that different than two "races" of humans having a child.