As a general rule of thumb active attacks can land about 3 or 4 blows before the Great Old One introduces a protective barrier to shield the cultists.

Your characters can still use these attacks, they just won't directly harm the cultists. It's hand to hand, machete to machete, even playing field.

Also passive powers, like shape-shifting or psychic illusions or barriers have an effective time of approximately 10 minutes

then the Great Old One interferes and the cultists will see through the illusion, disguise barrier, etc.

Like active attacks, the character still has their ability, it just becomes ineffective against the cultists directly.