EDIT: full list of affected abilities
Aerilate
Analytic
Aura Break
Battery
Beads of Ruin
Blaze
Chlorophyll
Contrary (negates boosts twice, resulting in no change)
Compound Eyes
Dark Aura
Defeatist
Dragon's Maw
Dry Skin (fire weakness)
Fairy Aura
Flare Boost
Flash Fire
Flower Fift
Fluffy (contact resist, fire weakness)
Friend Guard
Fur Coat
Galvanize
Gorilla Tactics
Grass Pelt
Guts
Hadron Engine (spa boost)
Heatproof
Heavy Metal
Huge Power
Hustle
Ice Scales
Iron Fist
Light Metal
Marvel Scale
Mega Launcher
Minus
Multiscale
Neuroforce
Normalize
Orichalcum Pulse (atk boost)
Overgrow
Pixilate
Plus
Power Spot
Prism Armor
Protosynthesis
Punk Rock
Purepower
Purifying Salt (ghost resist)
Quark Drive
Quick Feet
Parental Bond (2nd hit multiplier)
Reckless
Refrigerate
Ripen
Rivalry
Rocky Payload
Sand Force
Sand Rush
Sand Veil
Serene Grace
Shadow Shield
Sharpness
Sheer Force
Simple
Slush Rush
Sniper
Snow Cloak
Solar Power (spa boost)
Solid Rock
Stakeout
Steelworker
Steely Spirit
Strong Jaw
Supreme Overlord
Surge Surfer
Swarm
Swift Swim
Sword of Ruin
Tablets of Ruin
Tangled Feet
Technician
Thick Fat
Tinted Lens
Torrent
Tough Claws
Toxic Boost
Transistor
Unburden
Vessel of Ruin
Victory Star
It seems I was wrong about Adaptability. It just plain sets the STAB modifier, not multiplies it, and it's further supported by it giving a different boost when terastallized (9/8 instead of 4/3), so Adaptability is not affected by this meta. Edited post