The ability holder ignores abilities of the opponent when attacking. Abilities that make an opponent immune to a type of attack, such as Levitate, fail and get damaged as normal. Abilities that protect teammates such as Sweet Veil will also fail, even if the Pokémon with said ability is not the target. Abilities that prevent status conditions will fail giving that Pokémon that Status condition. However, most of these abilities also cure the status condition so, the Pokémon will recover the next turn. If the ability holder forces an opponent to switch out using a move that forces switches, the incoming Pokémon's ability is also ignored.
Mold Breaker will also ignore abilities even if the effect is beneficial, such as a Fire-type move on a Pokémon with Dry Skin. The ability holder also do not benefit from Flower Gift.