Why does this seem like a furry thread?
In games/movies/books, interspecies relationships exist because human beings aren't the only sentient, intelligent beings.
On the real world, planet Earth, there are no others.
I guess the key here is "consent". When you enter into an relationship, it's between 2 consenting individuals who desire one another. When you're plowing the neighbor's dog, there is certainly some kind of disconnect in "consent" there. As ludicrous as that person's imagination is, in trying to imagine the dog enjoying it, it just doesn't fit in with reality.
Mass Effect works because it's a different world, with established fictional rules, as with any large RPG world. In these worlds, there still exists racism, and discomfort, even when say an elf beds a nord.
In those fictional worlds, I would "support" (whatever that means) interspecies relationships or 'breeding', so long as it didn't create some sort of super-virus or mutant offspring every time they had sex.