Consider a recent article from the EFF regarding “Rapid DNA Analyzers”. The article poses the potetial issues involved, but also consider that any DNA collected (if not destroyed) would violate not just your privacy, but your entire blood line. What if DNA from immigrants were collected? Much of that information is inherited, so generations down the line, your privacy is still violated.
I cannot comment intelligently on the matter since I haven't read deeply enough into the proposed storage/hashing/etc policies, but those polices can be abused and such data can be leaked. I highly oppose any sort of DNA collection outside of personal at-home use (when the technology is available with free software) and use by medical professionals for personal medical reasons so long as the institution performing the test can provide stringent evidence of its destruction. But even then, if law enforcement somehow got a hold of the DNA before it were destroyed, then the problem still exists, so it would be best if you had your own personal tools to analyze your own DNA and distribute only the portions that were required (and encryption tools like GPG could be used for distribution).
One day, but not now. Let's make those scanners affordable and run free software.