I'm ~25.5 years old, and had a pretty healthcare oriented upbringing (I grew up in family of clinicians).
So I guess I'm not 100% dead set, but pretty close. If this tool was used in a healthcare context, by healthcare professionals I might consent to it. For example, if as part of my annual check up I filled out a list of the people I had intercourse with (and their location, DOB, some more identifiers) and the last time I did so, etc. and it got entered into the EHR, and then EHR did some linking (Epic EHR already has Care Everywhere which links records across health systems), then at least the data would be in the system. From there it could automatically send alerts out, or perhaps better, it would alert your physician/clinician that you might be of higher risk. I don't think the clinician (or any human user, besides the user them self) should be able to see who their self reported partners are.
So the above system makes the assumption that people have regular access to physicians, which is not a safe assumption. People who already have regular access should be getting screened by their clinician to see if they are at risk, and then tested. So I'm not sure it really has that much of a value add, and it certainly adds some complexity.
I'm all for reducing the burden of STDs/STIs, but I'm not sure that a registry is the best approach, but I'm not a health policy person.