As Van Ardsdale explains purity is not a genetic reality, first of all because each time a new person is conceived (by the enjoyable but quite impure act of sex) admixture takes place (and if mum and dad are genetically too similar, then inbreeding happens what is generally bad). So whoever would wish to imagine themselves as pure should not look into genetics but into Platonic solids or something.
But the right tools in the wrong hands typically has the wrong results. And the tool of genetic analysis in the hands of Hitler* or the like could be used to entice racist discrimination.
Nature reports that a Hungarian genetic testing company, Nagy Gén, has issued a certificate by which a person, a Hungarian Nazi member of the criminal Jobbik party, was said to have no Jewish nor Roma ancestry.
Nagy Gén scanned 18 positions in the MP’s genome for variants that it says are characteristic of Roma and Jewish ethnic groups; its report concludes that Roma and Jewish ancestry can be ruled out.
It's difficult to imagine how the company could certify that because there are no absolute lines defining such ethnic categories, not in the genetic aspect either, just clinal trends.
I understand from the context (18 positions) that the test is one of those biometric AIM-based tests that police uses sometimes to attempt to guess (without any certainty) the ancestry of suspects.
The scandalous certificate was first posted at a Nazi site, which praised the intent but (correctly) dismissed the scientific quality of the test. It was later republished at a Magyar-language news blog.
The affair underlines the dangers of all kind of biometrics, be them genetic or anthropometric, when used for reasons that are not pure science. That's a reason why I do not generally favor private, commercial genetic testing but rather academic studies of populations with prehistory reconstruction intent.
Personally I have never got myself tested nor I really care much because what matter for me is not "my" private ancestry but, if anything, the ancestry of the diverse peoples and communities, what can tell us something about their history and prehistory.
* Incidentally, I suspect that Hitler would have got serious problems promoting his racist ideas if he would have got access to genetic analysis because his paternal lineage was quite Mediterranean and ultimately rooted in Africa (it could even be Jewish, although hard to tell ultimately). He would have had to lie even to himself, abandon his racism or maybe kill himself (mostly good results).