Society will have to adapt to a better understanding that this is true. Keeping one’s DNA secret is not going to be a useful defense against ignorance of how DNA works.
The last 10,000+ years has not been static from my perspective. Blood testing came along. Limited DNA testing came along after that. Perfect DNA testing will be here soon. The technology won't care how you feel about it being used. I'm not imagining a mythical perfect future. I'm imagining a very real future that we can't avoid and need to deal with more pragmatically.
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