The claim that race doesn't exist is simply false. We can talk about whether or not it's useful to make policy decisions based on race, but if we're respecting the data, we can't say that there are no coherent human population groupings smaller than homo sapiens or that these groups do not align with traditionally-understood "race".
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1196372/
It's incredibly frustrating to see well-intentioned people just flatly deny facts about the world. The mistrust and resentment this denial causes makes it much more difficult to get useful messages across.
My assertion is that everyone is a mixture, which is true. People exist on a continuum of race without discrete borders[2].
1. http://www.scientificamerican.com/article/race-is-a-social-c...
2. http://www.nature.com/ng/journal/v36/n11s/full/ng1435.html
The issue 'race is correlated with X' is not materially affected by how exactly race (especially its borders) is defined and taxonomical problems - it's important in it's own regard, but in this regard, it's not the core problem, it's a red herring distracting from the core question of "does race affect X'; and that question is the same, with the same answers, no matter if in your analysis you choose to model race as discrete borders or as a continuum.
If your test can accurately group "Hispanics" which no-one actually claims is a race, then it doesn't prove that any other grouping it finds is a "race", however that is defined.