@Nrdsb4 -
I agree with you that use of the DNA he discarded at the murder scene and the DNA taken from anything he discarded in the present day that was used to match to the crime scene DNA is clearly legal and appropriate. The issue that may arise is with the method that was used to connect the two. How did the police know to follow HIM as opposed to anyone else around and try to get something he threw out present day to compare to the murder scene evidence? That link apparently came from the DNA uploaded by the relative to the public genealogy website. The potential issue is that, while the relative clearly surrendered his own, personal right to privacy, did the relative have the right to incriminate his kinsman by his choice to upload their shared genetic materials? Does any person have the right to privacy of their own genetic materials if they choose not to put them out there. That’s the question that I think will arise in the context of this prosecution.
In another context - what if a company that is considering writing a health or life insurance policy for you uses this website and finds that your uncle or first cousin has uploaded DNA indicating a family tendency towards cancer or some other debilitating illness and, based on that, decides to not write you a policy or charge you extra? You most likely wouldn’t think that was fair play. The issue here is very fraught because the man is accused of being a notorious serial killer and rapist (and he probably can’t be prosecuted for the rapes since the statute of limitations has likely long since expired, so any victim who could ID him was the victim of a crime he can’t be charged for), but the constitutional concern is the same.