I can speak from the computer side of that. No database is 100% safe, meaning that someone who shouldn't, might access it or that normal maintenance could contaminate it. If your DNA is in a database, that means they (most likely) have your name, birthdate, SSN, last know address, all relatives and who knows what else someone feels necessary to the identification of X person with X DNA. These records can get mixed up, especially when porting them to a new system (moving the records from one database to another). Over the course of a lifetime, some kind of update to the system will happen several times, each opening an opportunity for something to go wrong. (I know of an update of an RSO database that almost went severely wrong, except it was caught-barely-in time. I don't know if it ever got updated due to the problems with it.) From that point alone, I am wary.
As to it infringing on my privacy, it is nobody's business what my blood type, dna, ssn, phone number (if I don't want to give it), mother's maiden name, family status, or anything else is if it does not directly affect them at that time. Period. Just isn't. Will you tell me your real name and address and phone number here on line? No, because you have no idea who is looking at this. Same is true of any information you give to anyone. Just because someone works for a government agency doesn't make them trustworthy. There have been Govt people and LE who were not good people, how do I know if one of them might be looking at my DNA profile? Sure, some of that information is out there already, but I am more judicious than most about giving out my info, and I have a pretty good knowledge of which databases talk to each other, which ones don't, and which ones dump information on a regular basis.
Some would call it paranoid, some would call it safety conscious, but generally speaking, since I live in the USA and Freedom is supposed to be the cornerstone of what what the USA is all about, what is mine belongs to me, unless I choose to give it to someone else. Same with my DNA.