Kurama's origin timeline. Kaguya managed to rise again and unleashed a zombie apocalypse which killed everyone on the planet. Everyone.
Kurama himself for the Elemental Nations. They know exactly shit about him, they are unable to catch him, and he runs amok kidnapping living weapons of mass destruction and dangerously coming close to ignite another world war.
Kurama also represents a much more Adult Fear, as he primarily abducts the kid jinchurikis. Asshole as he is, it's easy to empathize with the Kazekage when his youngest son disappears within Suna's walls.
Added to this is the idea that a child can be in such a horrible situation that stranger danger flies out the window because the stranger is nice.
When Kakashi and Kurama end up fighting in Konoha's streets, the six-year-old Naruto tries to stop them by jumping between them, which prompts Kurama to throw himself on Kakashi's Raikiri to protect the kid. For one single moment, you could see Kakashi's horror at the possibility he may have killed Naruto's uncle in front of the boy.
This fear stays with him as the Freak Squad chases Kurama, with him pointing Naruto will grow to hate Konoha if Kurama is badly hurt or even killed when they will force them to come back - which is very likely to happen.
Most shinobi have their phobias played for comedy and lightness... except for Kurama who's terrified by the Sharingan because of its potent Mind Rape abilities which have repeatedly been used against him. Then the Freak Squad catches him, and Shisui almost uses his Kotoamatsukami on him while he's tied and helpless.
Orochimaru brings Uzumaki Kushina and Hatake Sakumo from the dead as a psychological weapon against their loved ones. Kakashi is suitably horrified when he has to fight his own father.
Konoha's Clans are horrified when Genma brings them proof that Danzo kidnaps their children to transform them into emotionless living weapons. Even worse is Aburame Torune confessing he willingly did go with Danzo because he didn't want his baby cousin Shino being abducted in his place.
Fuu is this to dojutsu users with her glitter technique. While being blinded in battle is something that terrifies every ninja, it is especially visceral for weilders of the Sharingan and Byakugan. Shisui, who actually is fond of Fuu and a general nice guy, cant help but mentally label Fuu as Abort Mission, Do Not Engage, after seeing her glitter technique in action.