Before I give a 10 second answer, please bear in mind that the idiom Not only....But also is used for lists in one/same direction.
For eg - Jim is not only handsome but also intelligent - CORRECT
For eg - Jim is not only humble but also insensitive - WRONG....Makes no sense. Humility and insensitivity are not related.
Coming back to the questionThe new house's front door is secured by an electronic lock;
a feature that not only allows residents to lock and unlock the door without physical keys, but also may prevent them from entering the house during a power outage.
(A) a feature that not only allows residents who lock and unlock the door without physical keys, but also may prevent --- INCORRECT IDIOM USE : first item is a useful feature but second item is a disadvantage
(B) a feature allowing residents without a physical key to lock or unlock the door, but also possibly preventing --- awkward. Does the feature work for all residents OR only for the ones without a physical key... Hmm
(C) a feature allows residents locking or unlocking the door without physical keys, but also possibly preventing ---- PARRALLELISM ISSUE : allows and preventing
(D) this feature allows residents to lock and unlock the door without a physical key, but may also prevent------ || and make sense. PLEASE NOTE we have not used NOT ONLY...BUT ALSO idiom here (for that the items should be in a single direction)
(E) this feature not only allows residents without physical keys to lock or unlock the door, but also prevents --- INCORRECT IDIOM USE : first item is a useful feature but second item is a disadvantage