(D) states that "someone who hears testimony that contradicts a long-standing opinion will generally entertain doubts about the source of the testimony rather than the correctness of the opinion." Applied to the information in the passage, this would mean that Sharon, who hears her favorite novelist speak out against a political candidate that Sharon herself has supported for years will doubt the novelist rather than the correctness of the novelist's opinion. The passage follows this, as Sharon's opinion of the novelist declines but her support for the political candidate does not waver. Therefore, this principle supports the information in the passage and is correct.
(E) states that "people are far less likely to renounce an allegiance that they have had for many years than to renounce an allegiance that is new to them." We know that Sharon has supported the political candidate "for years," but we lack any information regarding how long Sharon has supported her favorite novelist so we cannot necessarily say that this allegiance is "new." As a result, we cannot definitively say that Sharon supported the candidate before she supported the novelist. If Sharon supported the novelist first, the application of the principle would mean she would renounce the political candidate. This contradicts the passage and makes (E) incorrect. Also, the word "far" as used in (E) may be stronger than is necessary for the passage.
Does that make sense? Let us know if you have any other questions and best of luck with your studies!