And it is probably almost only caused by rape.
Agreed, I don't have a problem with stories that include serious topics in a serious way. Game of Thrones certainly isn't afraid to include rape in a reasonable dramatic way that demonstrates it's seriousness. It's complicated enough without crossing species boundaries. Ick.
It would be equally complicated to justify a consensual inter species romance. If that's your goal, fine, but the star crossed lovers should be your central story, not their unique offspring. In the WHF setting or AoS it would probably
There are two story reasons to have a half-breed. One is to showcase Man Versus Self inner conflict as your character deals with his or her dual natures. The second reason is to create a character who has abilities from multiple sources.
WHF and Age of Sigmar alike can make characters to fit either or both with magic. Wizards, gods, and creepy Moulder engineers can deliberately create hybrid creatures and there is enough randomness and unintended magic that you can have all sorts of magical mutant hybrids no one planned. You don't have to physically warp a being to make a cultural hybrid. In my own work, the humans of Turochlitan were biologically identical to the Old World humans but they were raised by Skinks. You can make a plausible scenario for almost anything raises anything, at least on a small scale. Besides raising another species from a young age, prisoner can suffer Stockholm Syndrome or deliberate brainwashing to become an agent of another species.
If you want hybrids, that's how I'd prefer to do it. The WHF is pretty complex and varied enough that it doesn't need hybrids. That said, I created cultural hybrids in my fluff-verse Turochlitan, a city of humans run by Skinks under the direction of a Slann. We've had more than a few good stories of Skaven experimenting with mutated Lizardmen to use as pawns as canon fodder. I wrote a short story that at least covers the early stages of a Dark Elf trying to do the same thing with a Saurus.
Anyway, I'd rather have magical or cultural hybrids than half A/half B creatures. Ick.