I don't think this is necessarily related to the Third Reich, but more about common sense. How much should a private company with the reach of Facebook and Google should collect about their users?
@thedaniel has it exactly right. The really dark shadow looming in German imaginations is the Stasi's.
Keep in mind, if you were 18 when the Wall came down, you're only 41 today, so these aren't vague or abstract fears. You actually grew up with the world's most terrifying police force running microphones into your apartment. To give you some idea of how pervasive they really were, the Stasi had one informer per 6.5 people, which is practically a spy in every family. By comparison, the Gestapo employed one secret policeman per 2,000 people.
As the article above notes, "It was widely regarded as one of the most effective and repressive intelligence and secret police agencies in the world." And no, you don't go from escaping that to ignorant bliss in half a generation.
