In some ways the Internet has afforded more privacy and security for people with STDs and people seeking more information about STDs. In other ways it has posed a great risk for those same people.
When you want to find out more information about an STD you no longer have to go see a doctor face to face. You can search for that information from the privacy of your home. A big barrier to getting tested and treated is the fear of embarrassment and since the Internet protects you from that I think more people will be getting the information they need.
The Internet has also provided a way to get treatment for STDs online through online pharmacy services. Now, STD infected individuals no longer have to risk the scrutiny of other people in the pharmacy when they get their prescriptions filled. Unfortunately, this online pharmacy option causes more of your personal information to be on the Internet where it is susceptible to hackers. People with STDs have to decide if the privacy of ordering from home is worth the risk of having their condition leaked to the whole virtual community.
One scary example of the Internet being used to breach the privacy of STD infected people is a site called STDcarriers.com. This site has a registry of STD infected people that are reported by other people online. To me this seems like a major human rights violation. If you are infected with an STD, it is your right to tell your partner when you are ready. Although some people don't handle their responsibility to their partner and don't tell them about their disease, it is still not someone's role to out them.
The issue with STDs is that unlike other diseases, STDs have a stigma attached. So its not just a risk of people finding out you are sick, but a risk of being judged for the type of disease you have. This is why privacy and secure information on the internet is essential to STD infected individuals.