Abilities bypassed by Mold Breaker

Aroma Veil (will the conditions be cured next action?)
Battle Armor
Big Pecks (immunity to defense drops from moves like Screech and Rock Smash)
Bulletproof
Clear Body
Contrary (reversal of stat changes caused by the Mold Breaker Pokemon)
Damp
Dry Skin (immunity to Water-type moves and extra damage from Fire-type moves)
Filter
Flash Fire
Flower Gift (BAP reduction to attacks from the Mold Breaker Pokemon)
Flower Veil
Friend Guard
Fur Coat
Heatproof (resistance to Fire-type moves)
Heavy Metal (use normal weight when calculating effects of the Mold Breaker Pokemon's moves)
Hyper Cutter
Inner Focus (immunity to flinch)
Insomnia (immunity to sleep; the sleep will be cured next action)
Keen Eye (immunity to accuracy drops from moves like Sand-Attack and Mud-Slap)
Leaf Guard
Levitate
Light Metal (use normal weight when calculating effects of the Mold Breaker Pokemon's moves)
Lightningrod (attacks still get redirected but do damage instead of boosting special attack)
Limber (the paralysis will be cured next action)
Magic Bounce
Magma Armor
Marvel Scale (BAP reduction to attacks from the Mold Breaker Pokemon)
Motor Drive
Mountaineer (immunity to damaging Rock-type moves)
Multiscale
Oblivious (the infatuation will be cured next action)
Sand Veil
Sap Sipper
Shell Armor
Shield Dust
Simple (doubling of stat changes caused by the Mold Breaker Pokemon)
Snow Cloak
Solid Rock
Soundproof
Sticky Hold
Storm Drain (attacks still get redirected but do damage instead of boosting special attack)
Sturdy
Suction Cups
Sweet Veil (the sleep will be cured next action)
Tangled Feet (evasion boost)
Telepathy
Thick Fat
Unaware (stat changes are not ignored when calculating effects of the Mold Breaker Pokemon's moves)
Vital Spirit (rank boosts and immunity to sleep; the sleep will be cured next action)
Volt Absorb
Water Absorb
Water Veil (the burn will be cured next action)
White Smoke (immunity to stat drops)
Wonder Guard
Wonder Skin