I have a lot of faith in the EFF but in this case I think they are confused. Our DNA is one of the least private aspects of ourselves. We share the vast majority of it with our family and even neighbors. The idea of hiding it is absurdly impossible. We leave it everywhere we go in quantities that are more than sufficient to completely reconstruct our genome. We would literally need to wear full body latex suits with filtered respirators to keep it private. In the medium term, the idea of having private DNA while living in a public environment is as incredible as desiring to have a public social experience while keeping your face completely hidden. DNA sampling arrestees is no more invasive than taking their photo. It is only our current technical capacity that makes us see the two as different.