So I was thinking about it.
Khorne. Chaos God of War, Blood, Mindless Violence and Slaughter, Carnage, Warriors, Brutal Honesty and etc. hates the whole psyker thing.
Yet at the same time he actually has psykers of his own. The whole Blood Pact Gore Mages being a thing and the Azariah Kyras situation, I came to the conclusion that Khorne doesn't hate psykers completely. In fact I dare say that he hates certain methods how psykers use their powers.
Remember, Sorcerers and Librarians are completely two different things. Sorcerers use runes, arcane devices and eldritch tomes to channel the powers of various Chaos Gods. Librarians on the other hand don't need those things to cast their powers. Librarians only have their willpower to channel the powers of the warp and without the help of bizarre warp artifact (except Rune Priests who are Imperial Sorcerers in all but name and use runes to cheat).
Khorne also hates manipulations and trickery (hence why he hates Tzeentch). Sorcerers are all about manipulations and trickery (especially Tzeentch ones). Librarians on the other hand don't need to even use their abilities to deceive and can simply spam smite at the enemy until there remains nothing.
So would actual Khorne Psykers be a thing if they used their own willpower to buff themselves/cast their powers to kill directly and instantly (remember, Khornates kill without spreading suffering in order to not empower Slaanesh) to slay in the Blood Gods name? Also as long as they won't manipulate/deceive and use typical sorcerer trinkets and devices?