This question tests us on parallelism concept. We need both sides of idiom "Not only X but also Y" parallel not only in form but also in logic. With this said, elements X and Y must be parallel to each other. Now that we have some basic understanding, let's jump on to options.
(A) not only influenced by diet and alcohol consumption, but also are by, - let's remove the fluff "not only INFLUENCED ... but also ARE BY". Here, the option tries to present INFLUENCED (a proper working verb) and ARE (a linking verb) parallel. But no, working verb cannot be parallel to a linking verb. Another issue here is the second element "the overall health of the human microbiome is ARE BY behavioral factors" - does not make much sense, right?
Eliminate
(B) not only influenced by diet and alcohol consumption, but also - in B we have "not only INFLUENCED ... but also BEHAVIOR FACTORS". In other words, not only VERB (influenced) but also NOUN (behavior factors). But verb and noun cannot be parallel. Moreover, second element, as in A, does not make a lot of sense to me "the overall health of the human microbiome is behavioral factors", huh? I hope you agree that this is nonsense,
eliminate.
(C) influenced not only by diet and alcohol consumption, but also are by - we have "not only BY DIET.... but also ARE BY" OR "not only prepositional phrase but also linking verb". No way can prepositional phrase be parallel to linking verb, nope. Besides, we again have nonsensical meaning in second element "the overall health of the human microbiome is influenced ARE BY behavioral factors". For whatever reason, we can safely
get rid of C(D) influenced not only by diet and alcohol consumption, but also by - we have "not only BY DIET...but also BY BEHAVIOR FACTORS", this one looks pretty good. It parallels prepositional phrase to prepositional phrase. Besides, the second element makes perfect sense now "the overall health of the human microbiome is influenced BY behavioral factors".
Keep D(E) influenced not only by diet and alcohol consumption, but also - ok, let's see "not only BY DIET but also BEHAVIOR FACTORS". Can we parallel prepositional phrase to noun? Certainly, no. Besides, again the second element of little sense "the overall health of the human microbiome is influenced behavioral factors", does not really work.
EliminateD is the best option.