BERLIN — German officials have been quick to ascribe the fury of their citizens over U.S. spying to their own history with the excesses of the surveillance state. But victims of the fearsome Communist East German secret police say: Not so fast.

Allegations that the National Security Agency kept tabs on Chancellor Angela Merkel’s cellphone communications have threatened counterterrorism cooperation, a major trade deal and good relations between the longtime allies. Popular distrust of the United States also is widespread.

Officials say Germans are sensitive about the issue because their society is still grappling with East Germany’s Orwellian spying apparatus, which was dismantled upon German reunification in 1990 but whose corrosive effects continue to eat at people’s lives....