The only mention of 'purity' in Nietzsche in this connexion is when he says [in Daybreak] that there are no 'pure' races [pure itself is an abstraction],races only 'become' pure.It is the Will to purity that emphasises racial/religious/cultural differentiation [look at the purity laws in the Old Testament etc.].Nietzsche says elsewhere that he does not want Germanic racial purity,but rather to create [by what he calls 'discipline and breeding'] a European race.

So race is a project of BECOMING.To Nietzsche ALL is in a state of flux,so purity,like stability is unattainable;but it is the will to purity,like the will to being [stamp being onto becoming] that is important.

Race is commensurate with Nietzsche's philosophy of Order of Rank.In the strict hierarchical organisation of Nietzsche's wont,the differentiated racial strata will not inter-breed.This will create,over time,racial differentiation-unavoidable fact of nature [called 'genetic drift';it's how you get different species of monkeys(!) ].

Get this;In a strict hierarchy without cross-breeding racial distance will come into being/becoming;this by the laws of evolution.Nietzsche expounds the laws of Manu because it details a technic for achieving this [incidentally it was the caste system which helped Hinduism to survive the onslaught of Moslem 'conversion' [or more properly,conquest].Order of Rank WORKS.Do you really think that our multi-cultural socities will survive once the Muslim world attains technological parity?No,there will be a return to Order of Rank-imposed from without.

Individualism is the real lie;no man is an island,and our speech,culture and very lives are based on familial context,with ancestors reaching back into the mists of time.Societies that misunderstand this have low birth-rates,soaring suicide rates and an underlying Nihilism.

Atomism is descending;Order of Rank [race] is ascending.