I guess the answer is D. It clearly communicates the meaning of the sentence

The OA is D. It from Kaplan 2015.

Why E is wrong? The use of "does" at the end is mandatory?

Yes, it is. Although it is allowed to omit repeated parts from the second element of a parallel structure, the omission is not allowed when the meaning is ambiguous. Without "does" at the end the sentence, there could be 2 possible meanings before omission (the blue font portions indicate the omitted parts from the second element of parallelism):

1. Total abstinence from alcohol does not correlate as strongly with good health as it (abstinence) correlates with moderate drinking.
2. Total abstinence from alcohol does not correlate as strongly with good health as moderate drinking correlates with good health.

The second one above is meant in this case and hence the usage of "does" is mandatory. The second sentence may also be written as (after removing the repeated part and replacing "correlates" with "does" to avoid repetition), the sentence becomes:
Total abstinence from alcohol does not correlate as strongly with good health as moderate drinking correlates does with good health.

Thanks! It makes sense to me now.

Recent surveys indicate that, contrary to popular belief, total abstinence from alcohol does not correlate as strongly with good health as with moderate drinking.

A. as strongly with good health as with moderate drinking
B. strongly with good health, like moderate drinking does
C. as strongly with good health as does moderately drinking
D. as strongly with good health as does moderate drinking
E. as strongly with good health as moderate drinking

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