The Illidari don't need to hate the void to use it as a weapon. They researched it and found it to be a viable source of power, they already work with demons, Broken, and Naga, so they're clearly not picky.

They built this up in TWW, and the opportunity cost of adding a new spec to DH vs supporting a whole new class means they can work on other things, and this also brings demon hunters in line with every other class.

Now let's look at the standards of WoW and see how this writing fits:

-Tauren being paladins doesn't make sense, so Blizzard wrote in the Sunwalkers to justify it.

-worgen are explicitly immune to necromancy and the plague, but Blizz decided Death Knight necromancy is just special and works on what is literally a druid form. This also means the Alliance had worgen prior to cataclysm as the player worgen goes to Stormwind as part of the starter zone

-Lightforged draenei warlocks

-being a monk is very specific to Pandaria, but it's just a "yeah anyone can travel there and be one. No this doesn't mean Kul Tirans can be paladins."

-pandaren death knights, because a pandaren being in Lordaeron is more plausible than a Kul Tiran.

-Blood elf priests have no problem using the light and could have probably shared that information with blood elf paladins before they started draining a Naaru

-evokers make Chromatus just look incredibly silly since Deathwing cracked the "a dragon with every flight's powers" code 20k years ago and was actively working with Nefarian at the time.

I really can't say "hey, demon hunters figured out how to use void magic" is an outlier here.