Big Data is no more of a threat to privacy than Small Town used to be.
That's both true and irrelevant. As any nerd who grew up pre-Internet in a small town can tell you, small towns are absolutely stifling places. One of the benefits of the Internet, for me, is that it allowed me to escape the ultra-conformist Midwestern suburban environment I grew up in and allowed me to communicate and interact with people who were (and are) different and not afraid of being different.
Our cultural roots lie in societies where supposed secrets traveled fast and
everyone knew if someone was pregnant or gay or searching for information
about strange topics.
You leave out the reason for those secrets traveling quickly: to most efficiently ostracize and isolate the person with the nonconformist beliefs, sexual orientation, religion, or what have you. This is all fine and pleasant, unless you happen to be the person about whom these beliefs are spreading.
Small towns are small, so a) the number of people who track you is also small; and b) you can go somewhere else. Big data is global. There is no escape.
In small towns, observation is symmetrical. You know who's doing what. But you also know who the gossiping busybodies are, and you know who talks to whom. Big Data is deeply hidden, with complex technical and financial relationships.
In small towns, relationships are, by dint of matching our evolutionary context, reasonably human. Big Data is by its nature depersonalized and abstracted. In person, people being creepy can get feedback that they are creepy. With Big Data, though, the only direct feedback they get may be increased profits.