Owners of Rottweilers have to contend not only with the disapprobation

Owners of Rottweilers have to contend not only with the disapprobation of family, friends, and neighbors, due in part to frightening portrayals of this much-maligned breed in movies such as The Omen but also with higher homeowner’s insurance rates or difficulty purchasing insurance at all due to the blacklisting of certain breeds deemed to pose a high risk for biting people.

The parallelism of correlative conjunctions is one of the most visible and identifiable errors before one proceeds further with other errors. In this case especially, with the ‘not only with’ … in the non-underlined part, it all amounts to whether there is a corresponding ‘but also with’ in the underlined part.

A) neighbors, due in part to frightening portrayals of this much-maligned breed in movies such as The Omen, but also with higher homeowner’s insurance rates or difficulty purchasing insurance --- maintains correct correlative conjunction parallelism. Correct choice.
B) neighbors, partly because of frightening portrayals of this much-maligned breed in movies such as The Omen, and with higher homeowner’s insurance rates or difficulty purchasing insurance – 'but only with' is missing

C) the neighbors, in part because movies such as The Omen have portrayed this much-maligned breed in frightening ways, as well as with higher homeowner’s insurance rates or difficulty purchasing insurance ----'not only with' … 'as well as with' is dead wrong


D) neighbors, partly as a result of frightening portrayals of this much-maligned breed in movies such as The Omen, but also higher homeowner’s insurance rates or difficulty purchasing it--- sadly misses ‘with' after but also.

E) neighbors, thanks in part to frightening portrayals of this much-maligned breed in movies such as The Omen, and with homeowner’s insurance problems, whether high rates or purchasing it --- no sign of 'but also with'.

This is an easy but wordy question.
Critical points to be checked are:
1) Idiom - "not only but also". ((Only option A & D use it properly))
2) "with" after "but also". ((Out of A & D, only A use it))

Therefore, Correct answer is A.

Owners of Rottweilers have to contend not only with the disapprobation of family, friends, and neighbors, due in part to frightening portrayals of this much-maligned breed in movies such as The Omen but also with higher homeowner’s insurance rates or difficulty purchasing insurance at all due to the blacklisting of certain breeds deemed to pose a high risk for biting people.

A "Not only with" must-have "but also with"

Only option A has this structure. Hence choose A

I hope it helps!