Why did the Jews of Sighet choose to believe the London radio reports rather than Moishe?

Moishe is the first character Wiesel introduces, thus setting up the ultimate struggle of the novel: maintaining faith through in the face of senseless evil.  This struggle begins when Moishe's credibility is stripped from him when he returns from being deported; his news is ignored for more reassuring news from the London radio. Wiesel suggests that people believe what they want to believe and ignore what scares them.   

Moishe is the spiritual foundation for the protagonist, Eliezer (based on Wiesel himself), guiding him through his studies of the Talmud and the Kabbalah (Wiesel, 21-23).  Wiesel juxtaposes Moishe's spiritual leadership with his lack of standing in society in the first two paragraphs.

"He was poor and lived in utter penury. As a rule, our townspeople, while they did help the needy, did not particularly like them.  Moishe the Beadle was the exception.  He stayed out of people's way.  His presence bothered no one.  He had mastered the art of rendering himself insignificant, invisible." Wiesel, 21

Wiesel continues to character Moishe as "awkward" and "waiflike"—elements that make him accessible and sympathetic to both the reader and his young student, Eliezer.  So far, he is simply a pitiable outcast with great faith. 

As the plot moves forward, we learn that Moishe, along with many others, is deported from Sighet (Wiesel, 24).  When he returns, he tries his very best to relate the horrors of the killing in the forest, but fails to elicit any sympathy from the content townspeople. 

"But people not only refused to believe his tales, they refused to listen.  Some even insinuated that he only wanted their pity, that he was imagining things.  Others flatly said that he had gone mad." Wiesel, 25

Eliezer admits that even he "did not believe [Moishe]" (Wiesel, 25).  These horrible things were happening far away and people often choose to turn a blind eye to evil because they are afraid. 

Therefore, Moishe, a once tolerated, humble, spiritual man, becomes the town madman, ignored.  He is passed over for a more reassuring source of news, the London radio, simply because that is human nature.