Have a look at my thread here. This explains all of these questions and common refutes. This is the backstory I use for my gnome demon hunter and guild. This backstory would work especially well for goblins and gnomes.
I’ll summarize why and how demon hunters can be possible as follows:
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Not apart of the Illidari, but an unknown secret organization that had been working to bring down the burning legion all along that utilizes soul harvesting technology.
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They utilize demon soul harvesting technology to gain power from demons, but never absorb demon souls directly into their body for safety. Goblins and Gnomes being intelligent. They could perfect this technology.
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The many worlds that the burning legion conquered still exist and their vast armies of demons still pose great threats. Someone from these vast conquered worlds could try to rise up and control the legion like Sargeras did? Demons still exist and pose a very strong threat in the world. Its just that the organization directing their goals has been dismantled.
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Demon hunters can fight all kinds of other threats. Demons can come in many forms. The fundamental thing you need to realize is that demon hunters were doing what they needed to stop one of the greatest threats to all of existent. If any such threat showed up elsewhere, they could do the same.
This explains how demon hunters could be possible for pretty much any race to become a possibility if blizzard wanted them to become such.