Propaganda can convince or repel. Social interactions can magnify these effects. We estimate the impact of Nazi marches in 1932 Hamburg, using granular data on all households. Direct exposure immediately affected voting -- propaganda was persuasive. To study diffusion, we measure social connections using contagion patterns from the 1918 Spanish flu, combined with social similarity. Nazi support spread to other parts of the city along the predicted contagion paths. Social spillovers are of similar importance as direct exposure. The marches were also polarizing the electorate â?? in opposition strongholds, they backfired, and gains were concentrated in areas with high Nazi support.