Throughout the movie Star Trek: Into Darkness, the issue of information privacy only comes up a few times. One of those times is in the beginning when we see a family whose daughter is in the hospital with a seemingly terminal disease. Our antagonist approaches the father, telling him that he has a way to make the daughter better. In this case, the antagonist has acquired the means to find medical information on members of the family so that he may blackmail a Starfleet officer.
Not much later, all of the Starfleet senior command, captains, and first officers are in a meeting at Starfleet HQ. They are being briefed on the information regarding the antagonist, John Harrison. They have access to all the information they could need about him so that they may track him down.
Finally, toward the middle of the movie, Spock confronts an officer who was “assigned” to the Enterprise. He has looked her up and found out that she is not in fact who she claims to be. This, again, is a good example of one’s ability to look up any information on an individual.
Now, out of these three instances, we can extrapolate a couple things. It is possible that this same society which no longer needs money also no longer feels the need for privacy, and all information is public. Alternatively, it is possible that in terms of privacy, the policies have not changed much. It is possible that the people in Star Trek are just as conscious about their privacy, and hold it just as dear as we do now.