There's no practical way to protect our genomes in meatspace. We're constantly shedding DNA into the environment. Hair, skin, saliva, etc. For example, an adversary can just tail us to a coffee shop or restaurant, and take a utensil or straw or napkin that we've used. And then submit the sample using a fake name, as investigators often do.

Edit: Those are excellent comments about scale. But generally, if you don't want to publicize your genomic data, just don't send in a sample.