Where the customer feels like their privacy is being violated. That is the line. Customers have expectations on what happens with their data, and those expectations need to be managed. Over time, they may change. But companies that start from a point of, what would a reasonable person want, are going to have an enduring approach.
In most cases, for analytics purposes, going deep on one single customer isn’t instructive. Analytics tends to look for broad trends across populations of folks. For B2B sales, or personalization, that is where analysis needs to be done on an individual level. However, that can still be done in a way that maintains privacy. Recommendations can be made inside a black box, with no logging. Apple does such an approach with their machine learning, doing it on device, to protect the consumer.