I would like my illidari to hide his demonic origin, but that is difficult with his appearance … would a demon hunter without horns or tattoos be acceptable?
There is an option in game to not have horns or tatoos, so presumably the answer is yes! However do consider a reason your character might skip on the tatoos. The tatoos are in fact magically imbued to help a demon hunter keep their inner demon in check, so maybe think of an alternative method your demon hunter might use if they choose to forgo said tatoos.
The tattoos and eye gouging are mandatory parts about becoming a Demon Hunter, so those are not something you can change.
However, the level of demonic corruption is variable. The amount of fel & corruption each demon hunter consumes can vary. This is why you have some Demon Hunters that look almost normal with just some blindfolds and tattoos; whereas you have others who have a truly demonic appearance.
Removing the tattoos would likely need a surgical intervention, and it would also negatively impact your power as a demon hunter as they impact your ability to resist magic(including corruption) and contain the fel energies within you.
The most convenient disguise would probably be illusion magic, perhaps your character has a background of being a mage; a mage friend, or just a handful of magical scrolls. Of course, paladins/other demon hunters would likely be able to sense your corruption; and the illusion wouldn’t work vs anti-illusion means, but it would fool most mundane eyes.
If memory serves, a Demon Hunter’s tattoos are mainly in place to help keep the influence of the fel they take in check. As such I imagine it would be excessively dangerous in universe to go without them. They are arcane in nature and act as a counter.
Demonic features are likely a result of the aforementioned fel influence. This is seemingly a natural result of fel corruption in general. While the degree of mutation among Demon Hunters differs by the individual, None that have been shown have looked completely normal and horns seem to be the most common demonic trait among them. Of course a DH without horns might be possible but I personally doubt one, at least in the Illidari mold, would not have at least some manner of visible corruption just by nature of the training.
In short, at least among the Illidari, due to how they do things and the nature of the power they work with, demonic mutation is likely inevitable and the tattoos are for their own good.
Pretty much everything the post above mine said with a little extra in places.
In order to preserve a bit of originality I’d like to share a personal example. My Night Elf Demon Hunter, Theara, is big into alchemy. She produces a variety of magical aromatics meant to affect people in a variety of ways. One of such affects one’s perception of her, allowing her to be seen as a relatively normal person.
There are also several examples, especially in Legion content, of demons disguising themselves. It wouldn’t be too far of a stretch to think that a Demon Hunter may have learned how to do the same, especially given their work entails the gathering of fel knowledge.
The burning eye sockets are kind of a giveaway. The Fel nature within is also going to be an unsettling factor. All connections to normality are part of what you sacrificed.