This may evidence may ignorance on the topic of genetics, but it seems to me that the natural response to increasingly prevalent/abused genetic profiling would be for both the criminal and noncriminal sector to begin pursuing crispr-like technologies to attempt to re-anonymize themselves? For the criminal sector, to reduce true positives, and for the non-criminal sector, to reduce false positives.
Would it even be possible to alter a person's dna enough to provide sufficient information entropy so as to make them 'unidentifiable' ala hashing without simultaneously introducing significant diseases/disorders? One could also hypothesize having such a process be performed continuously, such that a person might be constantly genetically unrecognizable from the organism they were the day before.
In other news, does anyone want to inject some venture capital into my new cryptographic genetic manipulation start-up? It's like a VPN, but for your dna.