Then they'd know that that person had a relative there. We're still a lot of dots away from going "Well, we found this DNA by accident, it was clearly and obvious Bob was there."
Based on the last 2 years of "show your papers" vaccine cards, I'm not sure why you'd pin this on Republicans.
Once they have a relative, it isn't that difficult to narrow it down to Bob. Think about it, you went from 350 million possible candidates to maybe 50 or less.
Go to the relative and ask them if they have any relatives in or near state X or city Y. That should narrow it down to a handful. And also you can narrow further by gender. Once you find a relative, you can logarithmically cull the search space.