As it is with traditional pharmacies, on-line drugstores rely on prescriptions to be successful, since it is primarily prescriptions that attract the customers, who then also buy other health-related items.
Option Elimination -
(A) As it is with traditional pharmacies, on-line drugstores rely on prescriptions to be successful - This is a trap answer as it uses the right "as" construction to introduce a subordinate clause but then sprinkles a significant pronoun error. The first "it" here is not the placeholder. If we ask the question, "What is with the traditional pharmacies"? It refers to the whole clause - online drugstores rely on prescriptions to be successful. This is wrong as the pronoun can only refer to a noun, not a clause, which makes this option wrong.
(B) As with the case of traditional pharmacies, on-line drugstores rely on prescriptions to have success - This choice also uses the right construction of "as" to introduce a prepositional phrase but then sprinkles an error. As a prepositional phrase, it's adverbial and needs to make sense with the subject of the following clause. So, it means online drug stores rely on, as with the case of traditional pharmacies. This doesn't make sense. Moreover, as RonTargetTestPrep also pointed out, we use "as is the case" or "or in certain cases," but as with the case is a weird construction.
(C) As is the case with traditional pharmacies, prescriptions are the cornerstone of a successful on-line drugstore - This is a bit different construction of "as" than the regular ones we are more accustomed to. But this still introduces a clause after "as." So, what is the case with traditional pharmacies? That the prescriptions are the cornerstone of success, and likewise, the prescriptions are the cornerstone of a successful online store. Correct meaning.
(D) As traditional pharmacies, so on-line drugstores rely on prescriptions to be successful - This usage of "as" is applicable when we say something like this - As the president, Tom fulfilled all his duties. So, we use "as" to show him in the capacity of a president. Here it doesn't make sense. "so," coordinating conjunction or what? Are we joining two independent clauses here? No.
(E) Like traditional pharmacies, the cornerstone of a successful on-line drugstore is prescriptions - Wrong. "traditional pharmacies" are compared with "the cornerstone."