Our Neanderthal cousins had a quixotic unmeasurable intelligence. The fine division of nature into tools, words, cleanly cut ideas and clear mosaics of cause and effect had no interest for them.
If you actually showed them a mosaic they would wonder why you ignored the rock-grain and the weight. Like someone gluing lego together. If you showed them a windmill they'd wonder why you were fucking with the currents. Show them a seed drill and they'd probably try to club you to death before it spread.
Neanderthals had no word for 'criminal'. These are the criminals they didn't have. Rare, but horribly dangerous and impossible to kill. The Science/Religion caste were practised super-shaman. High-level theoretical astral ramblers sang to the stars and the spaces between material things. They kept converse with the afterlife. The world of the dead was as far from them as America in the age of sail. When one turned bad, even if killed, they were coming back.
And when they turned bad they turned very very bad. Fascist/Animist soul-deep apocalyptics. Without political aims to fracture and encode the moral rot they went all the way wrong like man never has.
An answer was sought. The solution was harsh. Containment. The entire Neanderthal race combined to make themselves gradually extinct. The racial death-moan was encoded with harmonic traps. It held the souls and minds of it's bright-eyed shame. It holds them now.
But there was one hidden flaw. Accident or scheme no-one knows, but gene-key fragments dodged the trap before it closed. Careful, or accidental, interbreeding with a rising sub-species left rags of dissolute code dancing in alien flesh. If you have any of this code inside you, then you are a gate* and you can be used.
They are waiting now, hidden deep deep away from the sun. Ghosting and wandering like memories of abuse. A shameful unbidden thought locked within the earth. Fire-gold eyes like Saxon torcs, and rust-red mammoth coloured hair. Processing endlessly in the permanent night beneath your feet, fleeing the attention of the rock before it remembers what they are, and recalls the wrong they did to it. They are looking for you.
Meanderthals can whistle your soul out of your animal heart and eat it like meat while you watch. They do not, and never will, understand words. Mathematics can banish them in shivering fear. Any mathematics. Music is theirs, and movement, and dreams, religion and anything that transcends. They fear machines.
(Not truly fear. It's baffled rage-filled screaming incomprehension. It bothers them like surrealist art troubles a feverish child, but much much more.)
Meanderthals are vague spirits to most other races. They are a human problem and can touch us through the weave in our flesh. They want our help, or submission to get back and will offer and threaten what they can understand to do.
Meanderthals will assault you and cut out your soul with flint-knapped blades. (damage to WIS not HP) They will sing your spirit animal up out of your mouth, capture it and torture in in front of you. Their touch can make your organs revolt against each other like angry snakes in a bag. A single whistle can make oxygen revolt in self-contempt, forget it's bonds and incandesce the air in your lungs. They can bite through your skin and into the hopes you never speak, pulling them out in gobbets of your flesh. This is only the half-perceived relic of their powers.
If they capture you they may hang you from your heels, bleed you, and distil the blood with strange herbs. Gather round the bowl above the fire and inhale the pale red fumes, tasting out the sacred fragments. If you have a high WIS they may try to breed with you to produce viable young. Though such children have no more than an average chance of turning out 'evil'.
*Everyone who is not of direct African descent (probably, according to the internet) has some Neanderthal DNA. How far you want to go with this depends if it makes sense in your game and how you feel about the creepy/weird sub-scientific racial theorising. Technically, as written, pure Africans should be immune to Meanderthal influence.